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MODES  OF  RESEARCH 
IN  GENETICS 


♦The^^C^O 


THE  MACMILLAN  COMPANY 

NEW  YORK    •    BOSTON   •    CHICAGO  •    DALLAS 
ATLANTA    •    SAN   FRANCISCO 

MACMILLAN  &   CO.,  Limited 

LONDON  •  BOMBAY  •  CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  Ltd. 

TORONTO 


MODES  OF  RESEARCH 
IN  GENETICS 


BY 


RAYMOND   PEARL 

BIOLOGIST   OF   THE    MAINE    AGRICULTURAL   EXPERIMENT 

STATION 


THE   MACMILLAN   COMPANY 

1915 

All  rights  reserved 


COPTEIGHT,   1915, 

Bt  the  macmillan  company. 


Set  up  and  electrotyped.     Published  December,  1915. 


J.  S.  Gushing  Co.  —  Berwck  &  Smith  Co. 
Norwood,  Mass.,  U.S.A. 


PREFACE 

This  book  has  been  prepared  in  the  hope  that 
it  may  meet,  in  some  small  degree,  what  seems 
to  be  a  rather  definite  need  in  biological  literature. 
During  the  past  fifteen  years  there  has  been  a  great 
movement  of  biological  research  towards  the  prob- 
lems of  organic  evolution,  and  particularly  towards 
that  phase  of  those  problems  which  constitutes 
the  subject  currently  known  as  genetics.  Ex- 
perimental breeding  has  become  the  order  of  the 
day,  not  alone  in  the  laboratories  of  zoology  and 
botany,  but  in  the  agricultural  experiment  stations 
and  colleges  everywhere. 

Research  in  a  new  field  means  the  application  of 
new  methods.  Nowhere  has  this  been  more  true 
than  in  genetics.  For  a  critical  handling  of  many 
genetic  problems,  a  thorough  grounding  in  chem- 
istry, physics,  and  mathematics  as  well  as  biology 
is  really  a  necessity.  In  particular  the  widespread 
use  of  the  biometric  technique  in  biology  and 
agriculture  demands  a  clear  understanding  of  cer- 
tain fundamental  mathematical  principles.  Un- 
fortunately such  a  clear  grasp  of  underlying 
principles  is  too  often  plainly  lacking  in  the  bio- 


vi  PREFACE 

metric  work  which  is  being  turned  out  in  ever- 
increasing  volume. 

Demands  which  have  come  to  the  writer  from 
teachers  of  genetics  and  biometry  in  various 
agricultural  colleges  and  universities  for  separate 
copies  of  one  of  the  papers  reprinted  in  this  volume, 
in  order  that  they  might  put  it  in  the  hands  of 
their  students,  have  suggested  that  there  is  a  rather 
widespread  and  genuine  desire  to  examine  care- 
fully the  underlying  methodological  bases  of 
modern  genetic  science. 

It  is  hoped  that  the  present  volume  may  serve 
as  an  introduction  to  this  subject.  Even  though 
the  reader  may  not  agree  with  either  the  reasoning 
or  the  conclusions,  if  he  is  stirred  up  to  further 
thought  and  reading  about  the  matter,  the  purpose 
of  the  writer  will  have  been  served.  In  these  days 
of  extreme  specialization  and  great  activity  in 
biological  research  far  too  little  attention  is  paid 
to  the  fundamental  philosophical  background  of 
science. 

The  writer  wishes  to  acknowledge  his  indebted- 
ness to  Professor  H.  S.  Jennings  for  very  helpful 
suggestions  and  criticisms  in  regard  to  the  prob- 
lems discussed  in  Chapter  III,  and  to  Professor 
J.  McKeen  Cattell,  for  permission  to  reprint  from 
Science  and  the  American  Naturalist  such  por- 
tions of  the  book  as  have  already  appeared  in 
those  journals. 


TABLE  OF  CONTENTS 

OHAPTEB  PAQR 

I.    A   Critical   Examination  of   Current  Modes 

OF  Research  in  Genetics 
II.    BiOMETRic    Ideas    and    Methods    in    Biology, 
Their  Significance  and  Limitations 

III.  On  the  Nature  of  Statistical  Knowledge 

IV.  Certain  Logical  and  Mathematical  Aspects 

OF  THE  Problem  of  Inbreeding   . 
V.    Genetics  and  Breeding         .... 


Index 


42 
73 

101 
159 

179 


Vll 


MODES  OF  RESEARCH  IN 

GENETICS 


CHAPTER  I 

A  CRITICAL  EXAMINATION  OF  CURRENT  MODES 
OF  RESEARCH  IN  GENETICS  i 

To  any  one  interested  in  the  philosophical  bases 
and  methods  of  science  there  is  nothing  which  is 
regarded  as  sacrosanct  merely  because  traditional. 
In  theory,  of  course,  such  a  condition  of  affairs 
obtains  in  all  scientific  work,  and  the  implied 
state  of  mind  is  the  ordinary  one  of  all  scientific 
workers.  But  while  theoretically  science  is  free 
of  all  trammels  of  tradition,  practically  the  great 
bulk  of  scientific  work  is,  in  respect  of  its  methods, 
most  closely  bound  by  tradition.  Orthodoxy 
does  not  more  firmly  rule  in  the  vestry  than  in 
the  laboratory,  in  actual  fact.  Yet  every  one  will 
agree  that  a  real  and  permanent  step  in  advance 
in  science  is  only  taken  when  some  one  looks  at 
an  old  problem  and  at  common  facts  from  a  naive 
point  of  view,  and  applies  to  them  unorthodox 

^  The  substance  of  this  paper  was  read  before  a  club  in  Boston  on 
May  17,  1914.  It  has  since  been  modified  in  certain  minor  par- 
ticulars. 

B  I 


PROmiY  LIBRARY 

"'  C.  State  College 


2      MODES  OF  RESEARCH  IN  GENETICS 

methods  of  research.  I  shall  try  to  point  out, 
with  reference  to  an  old  problem,  where  it  would 
seem  that  current  methods  have  encountered 
definite  limitations  and  wherein  lies  the  special 
value  of  each.  If  I  can  succeed  in  doing  even  so 
much,  something  will  have  been  gained,  even 
though  it  is  not  now  possible  to  show  any  results 
achieved  by  new  points  of  view  and  new  methods 
in  the  field  to  be  discussed. 

The  problem  to  which  attention  is  invited  is 
one  of  the  most  fundamental  of  biology,  the 
problem  of  heredity.  In  what  is  to  follow  I 
shall  try  to  do  three  things. 

First:  to  define  the  problem  in  strictly  objec- 
tive terms,  free  if  possible  from  any  implications 
which  have  grown  out  of  theories  of  the  hereditary 
process. 

Second:  to  examine  critically  the  four  chief 
methods  of  investigation  by  which  attempts  have 
been  made  to  solve  the  problem,  endeavoring  to 
show  in  how  far  each  has  failed  to  take  us  beyond 
a  certain  point  in  our  understanding  of  the  matter. 

Third:  to  draw  such  conclusions  from  this 
methodological  critique  in  regard  to  the  most 
promising  lines  for  future  attack  as  seem  war- 
ranted by  the  results. 

I.   The  Problem  of  Heredity 

The  problem  of  heredity  can  be  easily  defined 
in  a  general  way  in  terms  which  are  perfectly 


A  CRITICAL  EXAMINATION  3 

objective.  It  is  a  matter  of  common  observation 
that  there  is  a  greater  or  less  degree  of  resemblance 
in  respect  of  all  sorts  of  traits  or  characteristics 
between  relatives,  and  in  particular  between  parent 
and  offspring.  By  heredity  is  meant  the  complex 
of  causes,  not  now  further  specified  or  defined, 
which,  taken  together,  determines  this  likeness 
or  resemblance  between  individuals  genetically 
related  to  each  other.  From  a  purely  formal 
logical  standpoint  the  problem  of  heredity  is 
the  problem  of  the  analysis  of  this  complex. 

The  difficulties  of  the  problem,  both  methodo- 
logical and  technical,  arise  from  certain  reasonably 
obvious  relationships  between  genetically  con- 
nected individuals.  In  order  to  see  what  these  are 
let  us  attempt  to  list  in  strictly  objective  terms, 
and  into  broad  categories,  what  is  actually  known 
about  the  relationship  of  two  individuals  standing 
in  the  genetic  series  as  parent  and  offspring.  For 
the  purpose  of  the  present  analysis  it  is  desirable 
that  the  categories  in  such  a  list  shall  be  broad  ones. 

The  phenomena  of  heredity  may  be  divided  in 
three  essential  categories.  These  may  be  listed 
as  follows : 

A.   Resemblance  between  adult  individuals. 

This  resemblance  is  the  central  observed  fact 
of  heredity.  Every  individual  organism  is  differ- 
ent in  some  degree  from  every  other  one,  but  any 
particular  individual  is  more  like  the  individuals 
genetically  closely  related  to  it,  than  it  is  like 


4      MODES  OF  RESEARCH  IN  GENETICS 

other  individuals.  This  resemblance  marks  the 
end  stage  of  heredity  regarded  as  a  process.  It  is 
unnecessary  to  cite  detailed  instances  to  prove 
how  extraordinarily  minute  and  specific  this 
resemblance  ordinarily  is,  in  respect  of  some 
one  or  more  characteristics  of  the  individual. 
Such  facts  are  matters  of  common  knowledge. 

B.  Gametogenesis.  The  intervention  of  a  rela- 
tively undifferentiated  stage  (the  germ  cell)  in  the 
cycle  of  reproduction  of  the  individual. 

In  higher  organisms  ordinarily  each  time  an 
individual  reproduces  itself  it  does  so  by  means  of 
a  single  cell,  which  separates  completely  from  the 
other  cells  which  together  make  the  individual. 
After  separation  this  cell  may  for  a  time  derive 
its  nourishment  from  the  individual  which  pro- 
duced it,  but  morphologically  and  physiologically 
the  completely  formed  gamete  is  essentially  a 
separate  and  independent  entity,  with  certain 
limitations  as  to  the  possibility  of  its  continued 
independent  existence. 

Gametogenesis  is  clearly  one  of  the  most  funda- 
mental parts  of  the  hereditary  process  for  two 
reasons :  first,  because  the  gametes  are  the 
essential  links  in  the  preservation  of  physical 
continuity  in  the  genetic  series ;  and  second,  be- 
cause, since  all  gametes  formed  by  the  same  in- 
dividual are  demonstrably  not  absolutely  alike 
in  respect  of  their  hereditary  qualities,  the  distri- 
bution of  the  different  hereditary  qualities  amongst 


A   CRITICAL  EXAMINATION  5 

the  several  gametes  must  be  determined,  proxi- 
mately at  least,  even  if  not  initially,  during  the 
process  of  gamete  formation. 

C,  Somatogenesis.  {Development  and  differentia- 
tion.) 

The  adult  offspring,  in  whose  adult  characters  we 
perceive  a  resemblance  to  the  parents,  is  the  result 
of  a  long  and  complicated  process  of  development 
and  growth  from  a  single  cell.  This  cell  is  itself 
a  composite  structure  produced  by  the  fusion  of 
two  cells,  one  derived  from  each  of  the  parents. 
From  the  standpoint  of  heredity  the  most  striking 
thing  about  the  fertilized  germ  cell  is  that  it  carries 
the  potentiality  of  producing  a  higher  degree  of 
differentiation  in  the  individual  which  develops 
from  it,  than  it  exhibits  in  its  own  structure. 
The  existence  of  such  potentiality  is  demonstrated 
by  the  specificity  of  the  developmental  behavior 
of  the  fertilized  egg.  Under  no  circumstances 
does  a  hen's  egg  ever  develop  into  a  turkey. 

While  the  germ  cell  is  distinguished  from  other 
cells  by  its  potentiality,  when  separated  from  other 
cells  of  the  body  and  appropriately  stimulated, 
to  develop  and  differentiate,  yet  it  must  be  recog- 
nized that  this  is  by  no  means  a  unique  property 
of  germ  cells.  Early  studies  on  regeneration 
and  the  development  of  isolated  blastomeres, 
and  the  recent  experiments  on  the  culture  in  vitro 
of  more  highly  differentiated  somatic  cells,  show 
clearly  enough  that  this  property  is  common  in 


6      MODES  OF  RESEARCH  IN  GENETICS 

greater  or  less  degree  to  nearly  if  not  quite  all 
living  cells.  The  distinction  between  germ  cells 
and  somatic  cells  in  this  regard  is  clearly  one  of 
degree,  not  kind. 

Of  much  greater  significance  from  the  stand- 
point of  heredity  than  the  potentiality  for  develop- 
ment, though  this  of  course  in  itself  constitutes 
one  of  the  fundamental  problems  of  biology,  is 
the  specificity  of  the  process,  at  once  unique  and 
manifold.  Not  only  does  any  particular  hen's 
egg  produce  always  a  hen,  but  it  is  also  a  par- 
ticular kind  of  a  hen  which  is  produced,  the  par- 
ticularity extending  to  the  most  minute  details. 

So  much  then  is,  in  general,  to  be  objectively 
observed  about  heredity ;  namely,  first  the  re- 
semblance between  genetically  related  adult  in- 
dividuals. Further,  this  resemblance  is  dependent 
upon,  because  inseparably  connected  with,  the 
two  processes  of  gametogenesis  and  somatogenesis.^ 

^  The  discussion  here  and  throughout  has  as  primary  material 
objects  of  the  reasoning  sexually  reproducing  multicellular  organ- 
isms. Fundamentally  it  would  appear,  however,  that  there  is  no 
essential  difiPerence,  so  far  as  the  elements  of  the  hereditary  process 
are  concerned,  between  such  higher  forms,  and  the  protozoa  or  other 
forms  reproducing  asexually  by  fission  or  other\\'ise.  Such  a  conclu- 
sion seems  certainly  justified  from  Jennings'  studies  on  inheritance 
in  Paramecium  reproducing  by  fission.  Cf.  in  particular,  in  this 
connection,  Jennings,  "Heredity,  Variation,  and  Evolution  in  Pro- 
tozoa. I.  The  Fate  of  New  Structural  Characters  in  Paramecium, 
in  Connection  with  the  Problem  of  the  Inheritance  of  Acquired 
Characters  in  Unicellular  Organisms."  Jour.  Exper.  Zool.,  Vol.  V, 
pp.  577-632,  1908. 


A  CRITICAL  EXAMINATION  7 

D.  From  these  observed  facts  two  definite 
inferences  are  not  only  plain,  but  indeed  inescap- 
able.    They  are : 

1.  That  germinal  substance  is  innately  possessed 
of  a  definite  and  particular  specificity,  which 
reaches,  in  degree,  to  the  order  of  the  individual, 
and  which  finds  its  most  obvious  objective 
expression  in  the  specificity  of  somatogenesis ; 
and 

2.  That  the  processes  of  reproduction  are  of 
such  a  sort  as  to  tend  to  maintain  this  specificity 
from  generation  to  generation. 

In  the  light  of  this  summary  analysis  of  elemen- 
tary facts  it  seems  clear  that  the  critical  problem 
of  inheritance  is  the  problem  of  the  cause;  the  ma- 
terial basis;  and  the  maintenance  of  the  somato- 
genic specificity  of  germinal  substance.  This  re- 
sult is,  of  course,  not  novel.  Though  somewhat 
differently  worded  here,  it  is  essentially  the  same 
conclusion  as  was  expressed  by  Conklin^  some 
years  ago,  by  Jennings,^  and  still  earlier  by 
Driesch.^ 

Before  proceeding  to  the  next  division  of  our 
program  I  should  like  to  digress  for  a  moment 
to  point  out  that  there  are  clearly  to  be  dis- 

1  Conklin,  E.  G.  "The  Mechanism  of  Heredity."  Science,  N.S., 
Vol.  27,  pp.  89-99,  1908. 

2  Loc.  cit. 

3  Driesch,  H.  "Zwei  Beweise  fiir  die  Autonomie  von  Lebens- 
vorgangen."     Verh.  V.  Intemat.  Zool.  Cong.,  Berlin,  1902. 


8      MODES  OF  RESEARCH  IN  GENETICS 

tinguished  different  orders  or  degrees  of  the  soma- 
togenic specificity  of  the  germinal  substance. 
This  fact  has  led  to  a  good  deal  of  confusion  in 
the  use  of  the  term  "heredity."  For  example, 
it  is  no  doubt  entirely  correct  to  say  that  birds 
have  feathers  because  this  sort  of  dermal  covering 
is  hereditary  in  the  class  of  animals  specified. 
But  heredity  in  this  sense  means,  both  theoreti- 
cally and  practically,  a  very  different  thing  than 
when  the  equally  true  statement  is  made  that  a 
Barred  Plymouth  Rock  female  inherits  the  barred 
color  pattern  of  her  feathers  from  her  sire  only, 
and  not  at  all  from  her  dam.  In  the  first  case 
one  is  dealing  with  a  phyletic  matter,  in  the  other 
case  with  a  sub-varietal.  It  is  obvious  that  the 
degrees  of  germinal  specificity  which  determine 
the  two  sorts  of  hereditary  phenomen  .  indicated 
in  the  example  must  be  of  widely  different  orders. 
One  represents  the  substratal  or  general  elemen^ 
of  heredity,  the  other  the  more  superficial  or 
individualistic  element.  It  is  obvious  that  the 
number  of  distinguishably  different  orders  of 
germinal  specificity  is  as  great  as  the  number  of 
distinguishably  different  orders  of  variability, 
which  in  turn  is  more  or  less  closely  reflected  in 
the  various  subdivisions  or  stages  in  taxonomic 
classification.  For  practical  purposes  of  thinking 
and  experimentation,  however,  it  is  suflScient  to 
distinguish  two  orders  of  germinal  specificity; 
namely,  a  general  and  a  special.    It  would  be  im- 


A  CRITICAL  EXAMINATION  9 

possible  practically  to  delimit  either  category 
precisely,  and,  for  present  purposes  certainly, 
this  is  not  necessary. 

We  may  now  turn  to  the  second  division  of  our 
program. 

II.   Methods  of  Research  in  Genetics 

1.    The  Biometric. 

The  biometric  mode  of  attacking  the  problem 
of  heredity  owes  its  inauguration  to  the  late  Sir 
Francis  Galton,  and  its  great  development  to 
Professor  Karl  Pearson.  Galton  was  the  first  to 
perceive  the  importance  of  dealing  with  heredity 
on  a  statistical  basis.  As  Pearson  has  well  said, 
the  recognition  of  this  fact  was  one  of  the  "greatest 
services  of  Francis  Galton  to  biometry."  Merz  ^ 
has  pointed  out  that  Galton  in  his  own  mind 
sharply  separated  the  problem  of  heredity  into 
two  parts,  the  one  having  to  do  with  the  material 
basis  of  hereditary  phenomena,  the  other  with 
the  phenomena  themselves.  His  early  experi- 
ments dealt  with  the  first  of  these  problems. 
By  means  of  blood  transfusion  he  hoped  to  test 
and  further  develop  Darwin's  theory  of  pangene- 
sis. Certain  now  obvious  technical  difficulties  of 
dealing  experimentally  with  the  problem  in  this 
way  undoubtedly  had  much  to  do  with  turning 
Galton  to  the  study  of  the  other  phase,  towards 

^  Merz,  J.  T.  "A  History  of  European  Thought  in  the  Nine- 
teenth Century,"  Vol.  II,  p.  613,  1903. 


10    MODES  OF  RESEARCH  IN  GENETICS 

which  his  own  inherited  instinct  for  the  statistical 
method  in  general  must,  in  all  his  thinking  about 
the  matter,  have  strongly  urged  him.  By  attack- 
ing the  problem  on  the  statistical  side  Galton 
felt  that  it  would  no  longer  be  necessary  "to  em- 
barrass ourselves  with  any  details  of  theories  of 
heredity  beyond  the  fact  that  inheritance  either 
was  particulate  or  acted  as  if  it  were  so."  ^ 

What  Galton  specifically  attempted  to  do  in 
attacking  the  problem  from  the  statistical  side  was 
to  measure  precisely  the  degree  of  resemblance 
which  obtains,  in  respect  of  different  somatic 
characters,  between  individuals  related  in  different 
ways  in  the  genetic  series.  His  primary  object 
was  to  determine  the  proportionate  contribution 
of  each  ancestor  to  the  individual's  inherited 
make-up.  The  only  practical  way  of  doing  this 
appeared  to  be  to  measure  the  degree  of  resem- 
blance between  individuals.  This  remains  to-day 
the  point  of  view  of  the  biometric  school  of  genetic 
study.  While  Pearson  has  introduced  many 
refinements  of  method,  and  has  taken  account  of 
various  modifying  factors,  such  as  assortative 
mating,  selection  and  the  like,  it  still  remains  the 
fact  that  in  his  studies  on  heredity  what  he  has 
primarily  been  concerned  in  doing  is  to  measure, 
by  the  method  of  correlation,  the  degree  of  re- 
semblance which  exists  between  relatives  of  dif- 
ferent sorts. 

1  Gallon,  F.    "Natural  Inheritance,"  p.  193,  1889. 


A  CRITICAL  EXAMINATION  11 

Gallon  himself  was  not  able  to  solve  com- 
pletely the  purely  mathematical  problems  in- 
volved in  his  study  of  heredity.  This  phase 
of  the  work  was  undertaken  by  Pearson  with 
brilliantly  successful  results.  He  developed  in- 
dependently a  very  complete  and  adequate  system 
of  dealing  mathematically  with  biological  data. 
His  results  in  this  direction  form  a  permanent 
and  epoch-making  contribution  to  the  working 
technical  equipment  of  science.  The  great  value  of 
these  results  for  the  future  development  of  biology 
is  not  yet  generally  realized.  Merz  compares  their 
significance  for  biology  to  that  of  the  mathemat- 
ical inventions  of  Fourier  for  physics.  I  should 
be  inclined  personally  to  rate  them  even  higher. 

Pearson  has  applied  this  technique  particularly 
to  the  study  of  inheritance.  The  chief  result  in 
his  hands  has  been  the  elaboration  of  Gallon's 
**Law  of  Ancestral  Inheritance."  This  law  as 
originally  stated  by  Gallon  was  as  follows:* 
*' There  was  found  an  average  (contribution)  of 
one  fourth  from  each  parent  and  one  sixteenth 
from  each  grandparent.  According  to  this  geo- 
metrical scale  if  continued  indefinitely  backward 
the  total  heritage  of  the  child  would  be  accounted 
for."  Pearson^  has  put  this  in  a  more  general  form 
which  does  not  restrict  the  values  of  the  fractional 

^  "Natural  Inheritance,"  p.  195. 

2  Pearson,  K.  "The  Law  of  Ancestral  Heredity."  BiometriJca, 
Vol.  II,  pp.  210-228,  1903. 


12    MODES  OF  RESEARCH  IN  GENETICS 

regression  coeflficients  to  the  values  given  by 
Galton,  which  were  admittedly  determined  from 
meager  material. 

Looking  critically  at  the  biometric  method  of 
studying  heredity  and  the  results  which  it  has 
achieved,  there  are  two  points  which  seem  partic- 
ularly to  require  discussion.  First,  it  appears 
clear  that  this  method  attacks  the  problem  at 
what  might  be  called  its  lowest  level.  In  other 
words,  the  biometric  method  deals  only  with  the 
element  of  the  problem  which  was  designated  as 
A  in  our  preceding  analysis  (cf.  p.  3).  As  it  has 
been  developed  in  the  hands  of  its  chief  devotees 
the  biometric  method  of  attack  fails  entirely  to 
recognize  any  real  or  essential  significance  to  the 
elements  B,  C,  and  D  of  our  analysis ;  that  is  to 
gametogenesis,  somatogenesis,  or  the  specificity 
of  the  germinal  substance.  Herein  lies,  in  the 
opinion  of  biologists  generally,  I  think,  the  chief 
weakness  of  the  results.  These  results  constitute 
essentially  no  more  than  a  rather  precise  de- 
scription of  the  most  superficial  external  features 
of  the  phenomena  of  heredity.  Except  only  in 
the  simplest  of  events  (and  then  not  directly) 
a  description,  however  minute,  of  those  events 
cannot  give  the  slightest  real  evidence  as  to  their 
cause.  A  scientific  visitor  from  another  planet 
might  describe  minutely  the  curious  polymor- 
phism to  be  observed  amongst  human  beings  in 
respect  of  the  amount  and  distribution  of  the 


A  CRITICAL  EXAMINATION  13 

hirsute  ornamentation  of  their  countenances, 
and  tabulate  vast  statistics  on  the  point.  Yet 
at  the  end  he  would  be  no  nearer  knowing  the 
cause  of  a  beard  on  Mr.  A's  face,  and  the  absence 
of  one  on  Mr.  B's,  than  when  he  began.  The  law 
of  ancestral  inheritance  seems  to  be  philosophi- 
cally in  much  the  same  case. 

It  should  be  noted  that  in  what  has  just  been 
said  I  am  referring  to  "description"  as  a  working 
method  of  research  for  the  acquisition  of  new  knowl- 
edge, not  to  "description"  as  a  general  philo- 
sophical category  constituting  the  means  of  ex- 
pression of  the  results  of  experience.  There  is 
obviously  a  real  distinction  here.  As  a  method 
of  science,  description  has  always  held  an  honor- 
able place  in  biology.  It  is  indispensable,  but 
not  complete  or  final.  The  function  of  the  de- 
scriptive method,  qua  method,  in  biology  would 
appear  to  be  essentially  only  to  establish  the 
basis  or  foundation  for  the  application  of  the  ex- 
perimental method,  which  is  the  only  strictly 
objective  analytic  tool  that  science  has.^ 

Description  as  a  general  mode  of  expression  of 
experience  takes  a  unique  place  in  Pearson's 
philosophy  of  science.  His  position  has  always 
been  that  all  science  is  nothing  but  description 
and    never    can    be    anything    else.     This    is    a 

1  Cf .  the  recent  valuable  paper  by  Jennings :  "  Causes  and  De- 
terminers in  Radical  Experimental  Analysis."  Amer.  Nat.,  Vol. 
XLVII,  pp.  349-360,  1913. 


14    MODES  OF  RESEARCH  IN  GENETICS 

defensible  position  and  has  been  so  universally 
adopted  as  to  have  become  almost  a  common- 
place of  scientific  thought. ^  It,  however,  has 
nothing  to  do  with  the  value  or  meaning  of  de- 
scription as  a  method  of  research. 

To  return  to  the  discussion  of  the  biometric 
method  in  genetics,  the  second  point  to  be  made 
concerns  the  reasoning  involved  in  the  use  of  the 
correlation  method  in  the  study  of  hereditary 
resemblances.  It  has  repeatedly  been  the  boast 
of  the  biometric  writers  on  this  subject  that  their 
results  were  absolutely  free  from  any  biological 
theories.  To  this  some  of  the  more  wicked  critics 
have  retorted  that  their  results  were  also  quite 
free  from  any  biological  significance.  Such  a 
criticism  is  not  true,  but  it  has  in  it  an  element  of 
verity.  The  reason  why  it  has  I  pointed  out  some 
years  ago  in  another  place,^  but  for  the  sake  of 
the  argument  it  may  be  sketched  here.  The 
essential  point  is  the  difficulty  of  interpreting  any 
correlation  coefficient  in  the  terms  of  the  causes 
which  led  to  its  existence.  Baldly  stated  the 
argument  of  the  current  biometric  method  of 
studying  heredity  is  this  :  Since  by  the  method  of 
correlation   the   degree   of   resemblance   between 

^  One  should  note  that  the  completely  restrictive  element  of  this 
view  is  by  no  means  universally  accepted.  Cf.  Royce's  Introduction 
to  Enriques'  "Problems  of  Science,"  Open  Court  Pub.  Co.,  1914. 

2  Cf.  injra,  chap.  II.  "Biometric  Ideas  and  Methods  in  Biology," 
pp.  42-72. 


A  CRITICAL  EXAMINATION  15 

parent  and  offspring  can  be  measured,  and  since 
heredity  is  a  cause  of  the  resemblance  between 
parent  and  offspring,  therefore  the  correlation 
method  measures  the  degree  or  intensity  of  in- 
heritance. This  argument  seems  sound  but  it  is 
really  specious.  For  heredity  is  not  the  sole  cause 
which  can  lead  statistically  to  a  significant  corre- 
lation between  parent  and  offspring.  Anything 
whatsoever  which  tends  to  bring  about  local  or 
group  differentiation  within  the  sample  included 
in  the  table  will  tend  to  produce  the  same  result, 
altogether  independently  of  any  genetic  relation- 
ship or  the  absence  of  it.  Such  possible  differen-  j 
tiating  factors  are  so  numerous  and  so  difficult 
of  detection  in  many  cases,  as  to  make  exceedingly 
dangerous  any  assumption  that,  in  a  particular 
case,  the  coefficient  of  correlation  is  a  measure  of 
heredity. 

The  essential  difficulty  here  is  just  as  real 
whether  one  goes  to  the  length  of  calculating  cor- 
relation coefficients  or  not.  The  logical  fallacy 
involved  is  particularly  insidious  in  the  case  of  at- 
tempts to  study  by  statistical  methods  alone  the 
problem  of  the  effects  of  selecting  fluctuating  vari- 
ations. Starting  with  heterogeneous  material,  as  all 
such  studies  except  those  on  self -fertilized  plants  or 
protozoa  have  started,  if  one  does  not  keep  an 
exact  pedigree  record  of  every  single  individual^ 

^  Furthermore,  it  is  not  enough  merely  to  keep  the  pedigrees.  The 
individual  pedigree-line-of-descent  must  be  the  unit  of  analysis  rather 


16    MODES  OF  RESEARCH  IN  GENETICS 

born  in  the  experiment  it  becomes  an  absolute 
logical  impossibility  ever  to  determine  critically 
whether  any  apparent  result  of  the  selection  is 
due,  on  the  one  hand,  to  a  sorting  out  of  preex- 
istent  hereditary  differences,  or,  on  the  other 
hand,  to  a  cumulative  change  in  the  hereditary 
determiners  themselves.  This  proposition  is  not 
only  absolutely  unassailable  from  the  logical 
standpoint,  but  that  it  is  also  practically  demon- 
strable, has,  I  think,  been  proved  by  Surface's^ 
analysis  of  the  Illinois  corn  work.  East's  and 
Hayes'  ^  selection  experiments  with  tobacco,  the 

than  the  correlation  table,  which  is  a  device  admirably  calculated 
under  certain  conditions  —  and  those  just  the  conditions  which 
obtain  in  the  study  of  selection  problems  —  to  obscure  to  the  point 
of  complete  concealment  facts  which  are  perfectly  clear  and  evident 
so  long  as  the  individual  is  made  the  unit  of  study.  To  lump  material 
into  a  correlation  table,  with  complete  loss  of  any  opportunity  there- 
after to  get  any  useful  knowledge  about  the  individual,  is  only  justi- 
fied when  from  the  nature  of  the  material  little  or  nothing  is  or  can 
be  known  about  the  individual  case  beyond  the  fact  of  its  occurrence. 
Then  may  we  properly  turn  to  the  statistical  method  as  a  last  resort 
in  the  search  for  knowledge.  But  surely  in  fully  pedigreed  material 
we  are  a  very  long  way  from  knowing  nothing  about  the  individual. 
On  the  contrary,  we  know  a  most  important  thing  about  each  indi- 
vidual ;  namely,  its  own  particular  ancestry. 

The  logical  points  regarding  the  statistical  method  here  touched 
upon  are  more  fully  discussed  farther  on.     (See  p.  69.) 

1  Surface,  F.  M.  "The  Result  of  Selecting  Fluctuating  Varia- 
tions." Data  from  the  Illinois  Corn  Breeding  Experiments.  IV^ 
Cong.  Int.  de  Genetique,  Paris  (1911),  pp.  222-237  (1913). 

2  East,  E.  M.,  and  Hayes,  H.  K.  "A  Genetic  Analysis  of  the 
Changes  Produced  by  Selection  in  Experiments  with  Tobacco." 
Amer.  Nat,  Vol.  XLVIII,  pp.  5-48,  1914. 


A  CRITICAL  EXAMINATION  17 

Hagedoorns'  ^  discussion  of  the  results  of  Castle 
and  Phillips'  -  on  piebald  rats,  Shull's  ^  analysis  of 
the  inheritance  of  capsule  in  Bursa  bursa-pastoris, 
and  finally  my  own  ^  studies  on  fecundity  in  fowls. 
It  should  be  clearly  understood  that  the  above 
criticisms  are  in  no  wise  directed  against  biometric 
methods  per  se,  as  weapons  of  research  in  attack- 
ing the  problems  of  genetics.  On  the  contrary, 
as  Galton  perceived,  statistical  methods  are  in- 
dispensable in  this  field.  These  methods  are 
indispensable,  in  this  particular  case,  because  a 
multitude  of  separate  and  distinct  causal  factors 
discretely  distributed  in  respect  of  their  action, 
are  concerned  in  the  determination  of  the  make-up 
of  the  adult  organism.  Since  the  locus  of  action 
of  all  of  these  factors  is  in  each  case  the  individual, 
it  is  impossible,  generally  speaking,  to  study  the 
action  of  any  one  factor  free  of  the  influence  of 

*  Hagedoorn,  A.  L.  and  A.  C.  "Studies  on  Variation  and  Selec- 
tion." Zeitschr.  f.  ind.  Abst.-  und  Vererhungslehre,  Bd.  XI,  pp.  145- 
183,  1914. 

2  Castle,  W.  E.,  and  Phillips,  J.  C.  "Piebald  Rats  and  Selection. 
An  Experimental  Test  of  the  Effectiveness  of  Selection  and  of  the 
Theory  of  Gametic  Purity  in  Mendelian  Crosses."  Carnegie  Insti- 
tution Publication  No.  195,  pp.  1-56,  3  plates,  1914. 

^  Shull,  G.  H.  "Duplicate  Genes  for  Capsule-Form  in  Bursa 
bursa-pastoris."  Zeitschr.  f.  ind.  Abst.-  und  Vererbungslehre,  Bd. 
XII,  pp.  97-149,  1914. 

^  Pearl,  R.  "The  Mode  of  Inheritance  of  Fecundity  in  the 
Domestic  Fowl."  Jour.  Exper.  Zool,  Vol.  13,  pp.  153-268,  1912. 
Cf.  also  earlier  papers  listed  in  the  bibliography  of  the  paper  here 
cited. 


18    MODES  OF  RESEARCH   IN  GENETICS 

all  others.  This  directly  implies  a  necessity  for 
the  application  of  statistical  methods.  It  means 
that  it  will  always  be  necessary  in  studying 
heredity  to  use  as  large  a  number  of  individuals 
as  possible  and  so  determine  average  effects  of 
the  different  causal  factors.  We  have,  of  course, 
in  genetics  a  special  case  of  the  general  proposition, 
more  fully  developed  in  a  later  chapter  (cf .  infra, 
pp.  54-61),  that  in  practice  the  statistical  method 
is  a  logically  necessary  adjunct  to  the  experi- 
mental method  generally. 

What  we  have  to  distinguish  clearly  between 
is,  on  the  one  hand,  the  biometric  school  of 
genetic  study,  which  stands  off  by  itself  in  sharp 
distinction  to  other  modes  of  attacking  the  prob- 
lems of  heredity,  and  which  is  criticized  in  what 
has  preceded ;  and,  on  the  other  hand,  the  statisti- 
cal method  as  a  general  method  of  science,  which 
as  such  is  indispensable,  as  well  in  the  study  of 
genetics  as  elsewhere. 

To  summarize :  it  is  believed  that  our  analysis 
has  shown  that  the  purely  statistical  mode  of 
attacking  the  problem  of  heredity,  as  it  has  actu- 
ally been  developed,  finds  its  chief  limitations  in 
that,  first,  it  deals  only  with  the  most  superficial 
aspects  of  the  problem,  and  second,  that  the  par- 
ticular method  pursued  is  based  upon  a  logically 
and  biologically  unsound  assumption.  At  the 
same  time  statistical  methods  in  general  are  found 
to  be  essential  in  dealing  with  the  problems. 


A  CRITICAL  EXAMINATION  19 

2.    The  Mendelian. 

From  a  methodological  standpoint  the  Men- 
delian mode  of  studying  inheritance  is  a  statistical 
method.  The  fire-eating  Mendelist,  if  any  more 
such  exist,  to  whom  biometry  is  anathema,  may 
object  to  this  statement,  but  a  little  consideration 
will  show  it  to  be  true.  In  actual  fact,  the  most 
essential  methodological  difference  between  the 
biometric  and  the  Mendelian  methods  is  one  which 
has  hitherto  been  quite  generally  overlooked,  so 
far  as  I  am  aware.  It  is  found  merely  in  the  fact 
that  the  biometric  method  studies  the  ancestry  of 
the  individual,  while  the  Mendelian  method  studies 
the  individual's  progeny.  One  goes  backward  on 
the  pedigree;  the  other  goes  forward.  The  net- 
work of  descent  may  be  likened  to  two  pencils 
of  light  rays  both  of  which  focus  in  the  individual. 
The  ancestral  pencil  converges  upon  the  individual. 
The  progenial  pencil  diverges  from  the  individual. 
The  practical  consequences  to  the  investigator 
of  the  fact  that  quite  different  possibilities  are 
opened,  according  to  which  one  of  these  two 
possible  ways  of  studying  genetic  relationships 
one  chooses,  are  extremely  interesting,  but  time 
is  lacking  to  go  into  their  discussion  in  detail  here. 
How  profound  in  general  they  are  is  sufiiciently 
indicated  by  comparing  the  achievements,  in  the 
way  of  advancing  our  knowledge  of  the  hereditary 
process,  of  the  biometric  method  on  the  one  hand 
and   the   Mendelian   on   the   other   hand.     It   is 


20    MODES  OF  RESEARCH  IN  GENETICS 

perhaps  too  much  to  say  that  the  law  of  segre- 
gation and  recombination  would  never  have  been 
discovered  by  study  of  the  ancestry  alone,  but 
such  a  result  would  at  any  rate  have  been  highly 
improbable. 

The  difference  in  viewpoint  between  the  bio- 
metric  and  Mendelian  methods  has  its  most  im- 
portant practical  consequence  in  the  fact  that  it 
renders  possible  the  application  of  the  experi- 
mental method  in  the  latter  case,  while  practically 
excluding  it  in  the  former.  One  can  experiment 
in  regard  to  one's  progeny  but  not  in  regard  to 
one's  ancestors.  Herein  lies  the  great  advantage  of 
Mendelian  method  as  a  mode  of  research.  While 
Mendelism  is  philosophically  a  statistical  method 
primarily,  as  has  already  been  pointed  out,  it  is 
not  solely  such,  but  instead  formulates  its  problem 
in  such  a  way  as  to  permit  the  experimental  mode 
of  attack. 

The  essential  thing  which  Mendelian  studies 
of  heredity  do  is  to  determine  the  distribution 
of  hereditary  differences  amongst  the  progeny  of 
a  particular  individual  or  pair  of  individuals. 
In  other  words,  it  studies  the  distribution  of 
hereditary  specificities.  This  is  obviously  a  higher 
level  of  attack  on  the  problem  than  the  biometric. 
Because  it  is  so  is  the  reason  that  it  has  been  so 
much  more  fruitful  of  results. 

That  the  method  is  essentially  statistical  is 
evident.     It    deals   with    masses   of    individuals. 


A  CRITICAL  EXAMINATION  21 

but  they  are  offspring  individuals,  not  ancestral. 
The  generations  which  the  Mendelist  discusses 
are,  in  Bateson's  now  universally  adopted  ter- 
minology, the  filial  generations.  From  the  stand- 
point of  mathematics  Mendelian  statistical 
methods  are  crude  and  simple.  Mendelism  has 
unfortunately  had  no  Karl  Pearson  to  work  out  a 
special  statistical  technique  directly  adapted  to 
the  requirements  of  its  data.  Such  a  special 
technique  may,  however,  be  expected  slowly  to 
develop  as  time  goes  on. 

I  should  like  to  digress  here  a  moment  to  dis- 
cuss a  particular  instance  of  the  crudity  of  current 
Mendelian  mathematics.  In  recent  developments 
of  Mendelian  theory  it  has  been  a  common  prac- 
tice to  assume  the  existence  of  multiple  factors  ^ 
as  the  causal  agents  of  a  single  character.  There 
can  be  no  a  ^priori  logical  objection  to  this  pro- 
cedure. Its  mathematical  dangers  are  not  usually 
perceived,  however.  Viewed  as  a  logical  method 
the  multiple  factor  hypothesis  is  simply  the  well- 
known  mathematical  procedure  of  increasing  the 
number  of  constants  of  a  theoretical  equation 
for  the  purpose  of  making  a  better  "fit"  to  the 
data  (in  this  case  the  observed  ratios).  But  any 
one  expertly  acquainted  with  the  general  theory  of 

*  This  hypothesis  was  first  used,  at  least  on  any  considerable  scale, 
by  Nilsson-Ehle,  "Kreuzungsuntersuchungen  an  Hafer  und  Weizen," 
Lunds  Univ.  Arsskr.,  N.  F.  Afd.  2,  Bd.  5,  pp.  1-122,  1909.  It  has 
since  been  widely  adopted  by  other  Mendelian  workers. 


22    MODES  OF  RESEARCH  IN  GENETICS 

curve  fitting  knows  that  this  process  always  runs 
a  grave  danger  of  becoming  perfectly  futile.  Be- 
cause if  one  increases  the  number  of  constants 
until  it  is  equal  to  the  number  of  classes  of  objects 
(ordinates)  to  be  fitted,  the  "fit"  is  bound  to  be 
perfect,  but  also  meaningless,  because  in  no 
sense  a  true  graduation.  This  danger  is  par- 
ticularly grave  in  Mendelian  work  because  there 
the  number  of  classes  or  categories  in  the  observed 
ratios  is  usually  small,  so  that  constants  and 
ordinates  may  very  easily  become  of  the  same 
order  of  magnitude.  In  this  event  agreement 
between  observation  and  theory,  however  close, 
affords  no  critical  evidence  whatever  as  to  the 
qualitative  validity  of  the  theory.  (Cf.  infra^ 
p.  29.) 

It  has  been  shown  by  Yule,^  Pearson,^  and  his 
students,  and  Hatai^  that  statistically  the  con- 
sequences of  the  distribution  of  hereditary  specifici- 
ties in  accordance  with  Mendel's  law  are  in 
essential  agreement  with  the  statistical  results  of 
the  law  of  ancestral  heredity.  This  result  is  at 
the  present  time  chiefly  of  interest  in  that  it 
furnishes  the  complete  proof  that  hereditary 
differences    are    distributed    in    accordance    with 

1  Yule,  G.  U.     "New  Phytologist,"  1902. 

*  Cf.  particularly  Pearson,  K.,  "Math.  Cont.  etc.  XII,"  "On  a 
Generalised  Theory  of  Alternative  Inheritance,  with  Special  Reference 
to  Mendel's  Laws."     Phil.  Trans.,  A.  203,  pp.  53-86,  1904. 

3  Hatai,  S.  "The  Mendelian  Ratio  and  Blended  Inheritance." 
Amer.  Nat,  Vol.  XLV,  pp.  99-106,  1911. 


A  CRITICAL  EXAMINATION  23 

those  fundamental  statistical  laws  to  which  other 
natural  phenomena  in  general  conform. 

The  most  important  achievement  of  the  Men- 
delian  method  has  been,  I  think,  the  demonstra- 
tion that,  on  the  one  hand,  hereditary  differences 
behave,  in  the  main,  as  discrete  units,  which  are 
shuffled  about  and  redistributed  to  individuals  in 
the  course  of  the  hereditary  process,  to  a  consider- 
able degree  independently  of  each  other;  and  on 
the  other  hand,  that  in  typical  cases  this  redistri- 
bution follows  the  simplest  of  statistical  laws  of 
dispersal,  the  point  binomial. 

Mendelism  finds  its  limitations,  just  as  did  the 
biometric  method,  in  the  fact  that  from  the  logical 
standpoint  it  is  essentially  a  statistical  method 
which  studies  only  the  laws  of  distribution  of 
things  given  or  assumed.  It  examines  only  the 
distribution  of  hereditary  specificities,  and  not  at 
all,  directly,  their  origin  or  determination.  The 
former  aim  cannot  be  the  goal  of  genetic  science. 
A  method  which  can  travel  only  so  far  cannot 
hope  to  say  the  last  word  in  the  discussion  of  the 
problem  of  heredity.  As  a  mode  of  research  the 
Mendelian  method  of  analyzing  the  progeny  dis- 
tributions rather  than  the  ancestral  will  always 
be  used.  It  was  indeed  one  of  the  most  brilliant 
methodological  discoveries  in  the  history  of 
science.  But  it  has  limitations  in  the  direction 
of  what  it  can  accomplish  per  se  in  elucidating  the 
problem  of  heredity.     Already  Mendelian  workers 


24    MODES  OF  RESEARCH  IN   GENETICS 

perceive  this  fact.  Thus  Spillman  ^  after  pointing 
out  that  the  facts  of  Mendelism  can  no  longer 
be  justly,  or  even  decently,  disputed,  goes  on 
to  say  {loc.  cit.,  p.  765)  :  "The  real  trouble  is  not 
with  the  facts.  It  is  with  the  interpretation  of 
these  facts.  Just  at  present  we  have  more  facts 
of  a  certain  kind  than  we  know  what  to  do  with. 
We  need  some  one  to  put  meaning  into  these  facts. 
We  are  in  the  position  of  a  man  lost  in  the  wilder- 
ness. What  he  needs  to  find  is  a  road.  It  does 
not  make  so  much  difference  where  this  road  shall 
lead,  for  all  roads  lead  to  each  other.  If  he  can 
find  any  road,  it  will  lead  him  to  where  he  can 
find  people,  and  these  can  point  out  other  roads 
leading  more  nearly  in  the  direction  he  wants  to 
go. 

"In  genetic  investigations  we  need  theories  that 
will  suggest  lines  of  investigation  that  will  be 
fruitful  of  results  —  that  will  lead,  not  to  more 
facts  of  the  kind  we  already  have,  but  to  new 
kinds  of  facts  that  will  throw  light  on  the  subject 
from  a  new  angle." 

3.    The  Cytological. 

In  the  field  of  genetics  cytology  is  practically 
concerned  with  a  single  phase  of  the  problem 
of  heredity,  namely  gametogenesis  {B  of  our  initial 
analysis)  and,  to  a  somewhat  smaller  degree,  with 
the  initial  stages  of  somatogenesis  and  the  fertiliza- 

1  Spillman,  W.  J.  "The  Present  Status  of  the  Genetic  Problem." 
Science,  N.  S.,  Vol.  XXXV,  pp.  757-767,  1911. 


^.  C.  State  College 


A  CRITICAL  EXAMINATION  25 

tion  of  the  egg.  The  broad  general  result  of  the 
investigation  of  this  problem  is  that  certain  defi- 
nite nuclear  components,  the  chromosomes,  are 
distributed  during  gamete  formation  in  a  manner 
which  parallels  the  distribution  of  hereditary 
characters  as  observed  in  Mendelian  segregation. 
In  other  words,  the  chromosomes  behave  in  game- 
togenesis  as  any  structures  which  were  the  bearers 
of  the  causative  agents  of  the  inherited  characters 
would  be  expected  a  priori  to  behave.  This  dis- 
covery is  clearly  one  of  first-class  importance. 
It  is  justly  to  be  regarded  as  one  of  the  greatest 
achievements  of  modern  biology.  It  furnishes 
strong  grounds  in  favor  of  the  basic  conclusion 
that  the  determination  of  hereditary  specificity 
is  resident  in  the  chromosomes.  The  familiar 
and  widely  accepted  doctrine  that  the  chromo- 
somes are  the  exclusive  "bearers"  of  hereditary 
qualities  is  a  crude  form  of  this  conclusion. 
Those  who  have  defended  this  doctrine,  however, 
have  been  compelled  from  time  to  time  to  qualify 
their  statement  of  it,  because  of  the  discovery  of 
facts  which  either  were  absolutely  difficult  to 
reconcile  with  it,  or  were  relatively  more  easily 
to  be  accounted  for  on  some  other  hypothesis. 

The  greatest  methodological  difficulty  in  the  case 
lies  in  the  fact  that  cytology  is  essentially  an 
observational  and  not  an  experimental  science, 
though  some  brilliant  beginnings  in  the  latter 
direction  have  been  made,  notably  by  Boveri. 


26    MODES  OF  RESEARCH  IN  GENETICS 

The  cytologist  is  compelled  by  force  of  circum- 
stances to  use  in  the  main  static  material  —  the 
dead  stained  cell.  But  in  the  problem  of  heredity 
he  is  concerned  with  dynamic  phenomena  — 
gamete  and  somsi  formation.  It  is  obvious  that  the 
chances  for  error  in  interpretation  are  very  great, 
and  difficult  to  eliminate  or  control,  when  one  is 
compelled  to  reason  from  a  static,  fixed  structure, 
to  a  dynamic  course  of  events. 

It  may  fairly  be  said  that  a  direct  connection  be- 
tween a  particular  chromosome  in  the  gamete  and 
a  particular  structure  in  the  adult  has  never  yet  been 
completely  demonstrated.  The  closest  approach 
to  it,  on  the  directly  cytological  side,  is  found  in 
the  case  of  the  sex  chromosomes,  and  here  a  causal 
nexus  is  not  absolutely  proven,  though  it  seems 
doubtful  whether  by  cytological  methods  alone  it 
will  ever  be  possible  to  get  essentially  nearer  to 
a  proof  than  we  now  are.  The  clear-cut  and 
thorough  researches  of  Wilson,  in  particular, 
and  American  cytologists  in  general,  on  the  sex 
chromosomes  appear  to  take  the  problem  as  far 
as  purely  observational  methods  can  take  it. 

There  has  been  no  lack  of  cytological  hypotheses 
regarding  genetic  phenomena  in  recent  years. 
In  particular  it  has  become  the  practically  uni- 
versal custom  to  look  for  the  explanation  of  diver- 
gent Mendelian  ratios  in  cytological  disturbances 
or  deviations  of  some  sort  or  other.  This  has  con- 
spicuously been  the  case  in  regard  to  the  so-called 


A  CRITICAL  EXAMINATION  27 

"linkage"  phenomena  of  inheritance.  The  diver- 
gent Mendelian  ratios  obtained  in  such  cases  have 
been  variously  explained.  Bateson  and  Punnett  ^ 
have  advanced  the  theory  of  reduplication  of 
germ  cells.  This  idea  was  first  suggested  in  the 
following  terms : 

"The  increase  in  number  of  the  two  types  of 
cell,  AB  and  ah,  may  be  reached  by  proliferation 
of  the  two  primordial  cells  of  those  two  types. 
It  may  further  be  remarked  that  though  the 
numbers  characteristic  of  coupled  systems  cannot 
be  produced  by  simple  dichotomies,  they  can 
readily  be  represented  as  produced  by  a  series  of 
periclinal  and  anticlinal  divisions.  For  example, 
if  AB^  by  periclinal  divisions  give  off  AB-,  and 
this  by  anticlinal  division  become  two  cells,  which 
again  divide  periclinally  and  anticlinally,  seven 
cells  AB  are  formed ;  by  repetition  of  the  same 
processes  15  are  formed,  and  so  on." 

The  direct  cytological  evidence  in  favor  of  the 
reduplication  hypotheses  would  seem  to  be  ex- 
tremely meager.  The  theory  can,  to  be  sure, 
point  to  cytological  observations  which  might 
furnish  a  basis  for  the  genetic  results  observed. 
But  this  is  a  very  different  thing  than  a  demon- 
stration that  they  do  furnish  such  a  basis. 

^  The  first  statement  of  the  reduplication  hypothesis  is  found  in 
Bateson,  W.,  and  Punnett,  R.  C,  "On  the  Interrelation  of  Genetic 
Factors,"  Proc.  Rotj.  Soc,  B.,  Vol.  84,  pp.  3-8,  1911.  Further  de- 
velopments of  the  theory  have  been  made  by  these  authors.  Trow, 
Bailey,  and  others  in  recent  papers  in  the  Journal  of  Genetics. 


28    MODES  OF  RESEARCH   IN   GENETICS 

One  cannot  escape  the  feeling  that  the  statistical 
ratios  themselves,  derived  from  experiment  and 
capable  of  direct  verification,  are  the  only  really 
definite  and  substantial  things  in  the  case.  The 
reduplication  theory,  in  spite  of  the  fact  that  it 
is  stated  in  cytological  terms,  appears  logically 
to  be  purely  a  statistical  hypothesis  for  the  gradua- 
tion of  a  particular  kind  of  observational  data. 
Logically  it  falls  in  the  same  category  of  operations 
as  fitting  a  curve  to  a  series  of  physical  observa- 
tions. To  this  no  objection  can  be  raised.  The 
only  point  is  that  any  one  who  has  had  experience 
in  the  mathematics  and  logic  of  graduating  ob- 
servational data  will  not  be  inclined  to  rate 
the  evidence  in  support  of  the  qualitative  cytologi- 
cal aspects  of  the  hypothesis  at  quite  so  high  a 
value  as  might  seem  at  first  thought  to  be  war- 
ranted. 

The  logic  of  the  case  is  possibly  worth  going  into 
a  little  farther,  since  it  involves  what  seems  to 
me  to  be  one  of  the  most  insidious  and  prevalent 
fallacies  in  biological  research. ^  An  investigator 
discovers  some  new  and  curious  facts,  which  are 
capable  of  numerical  expression.  He  then  frames 
an  hypothesis  to  account  for  them.     Depending 

^  One  wonders  how  prevalent  the  same  fallacy  may  be  in  other 
sciences.  The  writer  does  not  have  an  intimate  enough  familiarity 
with  the  actual  facts  to  form  anything  more  than  a  suspicion.  The 
suspicion  is,  however,  that  it  will  not  become  either  the  physicist  or 
the  chemist  to  assume  airs  of  superiority  over  the  biologist  on  this 
point. 


A  CRITICAL  EXAMINATION  29 

on  the  nature  of  the  data  and,  perhaps  even  more 
on  the  nature  of  the  person  handhng  them,  this 
hypothesis  may  take  a  directly  mathematical 
form,  as  say  the  equation  of  a  curve,  or  it  may  be 
seemingly  quite  unrelated  to  anything  mathemati- 
cal —  as  for  example  chemical,  cytological,  psy- 
chological, or  what  not.  What  the  hypothesis  is 
does  not  matter,  except  in  this  respect  that  it  always 
somewhere  involves  a  statement  or  implication  as 
to  the  qualitative  cause  of  the  quantitative  phenomena 
observed.  The  next  step  in  the  investigation  is  to 
calculate  out  for  each  particular  observed  case  the 
numerical  results  to  be  expected  on  the  basis  of 
the  hypothesis.  These  "expectations"  are  com- 
pared with  the  observations.  If  the  agreement 
is  good,  the  investigator  is  likely,  and  here  lies 
the  fallacy,  to  draw  the  conclusion  that  this 
agreement  proves  that  the  qualitative  assumptions 
made  in  the  hypothesis  are  correct.  Of  course 
the  agreement  logically  proves  nothing  of  the 
sort.  The  reason  why  it  does  not  is  found  in  the 
lack  of  uniqueness  in  the  quantitative  relations  of 
qualitatively  distinct  natural  phenomena.^  Be- 
cause two  series  of  events  follow  the  same  curve  it 
by  no  means  follows  that  they  are  due  to  the  same 
cause.     A  reasonable  accordance  of  the  numerical 

1  It  should  be  pointed  out  here  that  in  the  present  development 
of  this  argument  I  am  drawing  freely  from  a  previous  paper  (Amer. 
Nat,  Vol.  XLIII,  pp.  302-315,  1909),  in  which  the  same  point  was 
discussed  in  relation  to  investigations  on  growth. 


30    MODES  OF  RESEARCH  IN  GENETICS 

consequences  of  a  particular  hypothesis  with  the 
observed  data  does  not  prove,  in  the  absence  of  an- 
other hind  of  evidence,  that  the  hypothesis  ex- 
presses the  causal  basis  of  the  phenomena.  If  an 
hypothesis  is  true  its  numerical  consequences  must 
accord  with  observation  :  but  the  converse  proposi- 
tion that  because  there  is  agreement  the  hypothe- 
sis must  be  true,  does  not  necessarily  follow.  It 
is  one  of  the  weaknesses  of  the  human  mind  to  fall 
into  the  error  of  thinking  that  it  does  :  it  is  a  mis- 
take most  of  us  have  made  in  one  form  or  another.^ 
Bateson's  reduplication  hypothesis  seems  to 
furnish  an  excellent  concrete  illustration  of  the 
point.  Essentially  the  only  evidence  in  favor  of 
the  hypothesis  is  that  derived  from  the  agreement 
between  observed  and  expected  statistical  ratios. 
This  is  totally  inadequate  to  base  any  cytological 
hypothesis  upon.  Some  other  kind  of  evidence 
must  be  forthcoming  before  it  can  be  demonstrated 
that  some  gametes  "reduplicate"  to  a  just-suflS- 
cient  degree  to  meet  the  exigencies  of  the  case. 
An  ingenious  mathematician  could  probably  frame 

^  One  learns  to  be  cautious  about  "expectations."  There  once 
came  to  my  attention  some  results  put  together  by  a  non-mathe- 
matical biologist,  who  had  elaborated  a  very  complicated  mathe- 
matical hypothesis  to  account  for  his  observations.  The  agreement 
was  wonderfully  close  between  "observed"  and  "expected."  Some 
of  its  significance  disappeared,  however,  when  it  was  found,  upon 
analysis  of  the  hypothesis,  that  the  mathematical  methods  involved 
were  such  that,  barring  an  arithmetical  error,  there  could  by  no  pos- 
sibility ever  be  more  than  a  fractional  discrepancy  between  observation 
and  calculation,  whatever  the  nature  of  the  observations ! 


A  CRITICAL  EXAMINATION  31 

a  dozen  other  hypotheses  which  would  "fit" 
these  aberrant  ratios  equally  well.  Furthermore, 
if  he  were  also  a  biologist  he  could  no  doubt  give 
each  hypothesis  a  cytological  flavor,  and  bring 
forward  observations  upon  the  chromosomes  or 
other  cell  constituents  in  its  support. 

It  is  important  in  this  same  connection  to  con- 
sider carefully  the  results  of  Morgan  regarding 
linkage  phenomena.  He  and  his  students  ^  have 
collected  a  great  body  of  data  regarding  "linked" 
inheritance  in  Drosophila,  which  they  interpret 
on  an  hypothesis  which  locates  the  causal  de- 
termining factors  for  particular  characters  not 
merely  in  particular  chromosomes,  but  further  in 
particular  places  in  the  chromosomes.  The  in- 
genuity and  keenness  of  insight  displayed  in  the 
experimental  analysis  by  which  these  results  have 
been  obtained  must  compel  the  unreserved  ad- 
miration of  any  one  who  carefully  examines  them. 
This  Drosophila  work  will  stand  as  a  masterpiece 
of  experimental  research.  Logically  considered 
the  evidence  in  favor  of  the  chromosomal  hypothe- 
sis adopted  by  Morgan  is  based  primarily  on  the 
general  fact  that  the  chromosomes,  if  they  be 
assumed  to  behave  in  certain  postulated  ways, 
would  furnish  a  mechanism  which  would  account 
for  the  observed  breeding  results.     The  primary 

^  In  a  series  of  papers  appearing  during  the  last  few  years  in  the 
Jour,  of  Expt.  Zool.,  Science,  Amer.  Nat.,  Zeitsch.  ind.  Abst.- 
Vererb.  Lehre,  etc. 


32     MODES  OF  RESEARCH   IN   GENETICS 

objective  data  are  the  statistical  results  of  Mende- 
lian  experiments.  But,  and  herein  seems  to  me  to 
lie  the  logical  as  well  as  the  factual  superiority  of 
Morgan's  view  over  that  of  Bateson  and  Punnett, 
pains  have  been  taken  at  every  step  to  check  the 
hypothesis  by  direct  cytological  observation  as 
well  as  experimental  evidence.  The  net  result 
is  that,  up  to  the  present  time,  everything  that  is 
known  about  the  cytology  of  the  germ  cells  in 
Drosophila  is  in  entire  and  complete  accord  with 
Morgan's  interpretation  of  the  experimental  results. 
The  manifoldness  and  complexity  of  these  experi- 
mental results  have  now  become  so  great  as  to 
make  it  extremely  improbable  that  this  agree- 
ment between  cytological  and  experimental  data 
is  fortuitous.  On  the  contrary,  the  evidence 
comes  extremely  close  to  a  logically  complete  ex- 
perimental demonstration  of  two  points  ;  namely, 
(1)  that  the  factors  which  have  a  differential 
effect  in  the  determination  of  inherited  characters 
are  contained  in  the  chromosomes,  and  (2)  that 
the  factors  have  a  linear  arrangement  in  these 
bodies. 

The  extraordinary  difficulty  of  adducing  any- 
thing like  complete  proof  for  the  location  of 
hereditary  determiners  in  morphologically  definite 
elements  of  the  cell  organization  must  be  obvious 
to  any  one.  The  evidence  is  bound  to  be  largely 
of  an  inferential  character.  On  that  basis  the 
weight  of  evidence  now  available  strongly  indi- 


A  CRITICAL  EXAMINATION  33 

cates  that  the  chromosomes  are  directly  and  pri- 
marily concerned  in  the  distribution  and  trans- 
mission of  hereditary  differences.  This  does  not 
mean,  however,  that  one  can  unreservedly  assert 
that  the  chromosomes  are  the  exclusive  agents  in 
hereditary  determination.  On  the  contrary,  there 
are  a  number  of  facts  recorded  in  the  literature  of 
cytology  which,  in  the  light  of  present  knowledge, 
can  only  with  great  difficulty,  if  at  all,  be  recon- 
ciled with  such  a  view.  In  this  connection  it 
should  be  pointed  out  that  the  most  acute  and 
philosophical  students  in  this  field  no  longer  re- 
gard the  determination  of  hereditary  specificities 
as  probably  confined  exclusively  to  a  single  mor- 
phological element  of  the  cell.  Thus  Wilson  ^  has 
recently  said:  "In  any  case,  the  conclusion  is 
not  to  be  escaped,  I  think,  that  the  whole  cell 
system  is  directly  or  indirectly  involved  in  the 
production  of  every  hereditary  trait.  To  treat 
the  chromosomes  as  if  they  were  central  governing 
or  controlling  factors  in  the  cell  is  a  procedure  of 
more  than  doubtful  expediency.  For  the  present, 
at  least,  all  the  requirements  of  investigation  are 
sufficiently  met  if  we  think  of  the  chromosomes, 
or  that  which  they  carry,  only  as  differential  factors 
in  heredity,  not  as  its  primary  or  exclusive  'de- 
terminers.' Whether  they  possess  a  significance 
more  fundamental  than  this  is  a  question  that  may 

^Wilson,  E.B.     "Heredity  and  Microscopical  Research."  Science, 
N.  S.,  Vol.  37,  pp.  814-826,  1913. 

D 


34    MODES  OF  RESEARCH  IN  GENETICS 

well  await  the  results  of  further  inquiry."  Minot^ 
expressed  essentially  the  same  conclusion  in  one 
of  his  Jena  lectures.  Doncaster  ^  after  reviewing 
the  matter  says  that  the  evidence,  *' while  not 
proving  that  the  chromosomes  are  directly  con- 
cerned in  the  transmission  of  inherited  characters, 
makes  such  a  hypothesis  very  plausible.  Much 
unnecessary  confusion,  however,  has  arisen,  from 
stating  the  hypothesis  in  the  form  —  'the  chromo- 
somes are  probably  the  bearers  of  inherited 
characters.'  Evidence  has  been  adduced  that 
the  cytoplasm  plays  some  part  in  determining 
these  characters,  and  it  has  therefore  been  main- 
tained that  the  statement  is  disproved.  No  one, 
however,  would  suppose  that  the  chromosomes 
could  act  alone;  they  must  act  in  and  by  their 
relation  with  the  cytoplasm,  and  if  the  cytoplasm 
is  that  of  a  different  species,  the  total  ejffect  must 
necessarily  be  different." 

To  summarize  this  section  of  the  paper,  it  may 
be  said  that  while  cytology  attacks  directly  one 
of  the  basic  elements  of  the  problems  of  heredity, 
gametogenesis,  it  finds  immediate  and  serious 
limitations  in  two  facts.  The  first  is  that  the 
method  of  research  in  cytology  is  the  morphologi- 

iMinot,  Charles  S.  "Modern  Problems  of  Biology,"  Philadel- 
phia, pp.  1-123,  1913. 

2  Doncaster,  L.  "Chromosomes,  Heredity  and  Sex:  A  Review 
of  the  Present  State  of  the  Evidence  with  Regard  to  the  Material 
Basis  of  Hereditary  Transmission  and  Sex-Determination."  Q.  J. 
Micr.  Scl,  Vol.  59,  pp.  487-521,  1914. 


A  CRITICAL  EXAMINATION  35 

cal,  observational  method.  It  is  essentially  a 
static  method.  It  labors  constantly  under  the 
very  serious  danger  of  error  which  inheres  in 
inferring  the  course  and  nature  of  dynamic 
events  by  observation  only  of  their  static  ante- 
cedents or  consequences.  In  the  second  place, 
the  technical  difficulties  of  the  material  make  it, 
in  most  instances,  practically  impossible  to  apply 
the  experimental  method  directly  to  the  cytological 
side  of  the  problem  of  heredity.  In  spite  of  these 
limitations,  cytology  has  made  and  will  continue  to 
make  fundamental  contributions  to  the  progress  of 
research  in  heredity.  It  is  one  of  the  essential 
methods  of  investigation  in  this  field. 

4.  The  Embryological. 

Embryology  has  chiefly  been  cultivated  for  its 
own  ends,  which  are,  on  the  one  hand,  those  of 
descriptive  morphology  and,  on  the  other  hand, 
those  of  a  special  field  of  physiology,  Entwich- 
lungsmechanik.     Only  in  a  relatively  small  pro- 
portion of  instances  has  it  been  directly  and  pur- 
posefully used  as  a  mode  of  research  in  genetics. 
Yet  embryology  is  the  science  of  somatogenesis,^ 
which  was  shown  at  the  beginning  to  be  one  ofj 
the    fundamental    elements    of    the    problem   of 
heredity.     It  is   a  little   difficult   to   understand, 
why,  with  such  splendid  opportunities  as  the  em- 1 
bryological  method  offers,  so  little  light  regarding  \ 
the  hereditary  process  seems  to  have  come  from 
the  embryologist.     To  say  this  is  not  in  the  least 


36    MODES  OF  RESEARCH  IN  GENETICS 

to  depreciate  the  value  of  what  has  been  gained. 
The  studies  of  the  last  twenty  years,  particularly 
in  the  fields  of  experimental  embryology  and  cell 
lineage,  have  accumulated  a  splendid  mass  of  data 
regarding  the  principles  of  somatogenesis.  From 
the  standpoint  of  genetics,  however,  this  material 
is  in  a  scattered  and  diffuse  state.  What  it  needs 
is  a  synthetic  treatment,  in  which  all  of  the  now 
scattered  facts  of  experimental  embryology  shall 
be  brought  together  and  their  relations  to  the 
general  problem  of  heredity  clearly  shown.  A  few 
embryologists  have,  to  be  sure,  contributed 
notably  in  this  direction,  chiefly  in  this  country 
Brooks,  and  later  Conklin,  who  seems  to  me  in 
all  his  work  to  have  perceived  more  clearly  than 
any  other  recent  student  in  this  field  that  embry- 
ology has  a  very  important,  if  not  indeed  its  chief 
philosophical  significance  as  a  mode  of  attacking 
the  fundamental  problem  of  heredity.  In  this 
same  connection  the  recent  work  of  Gurwitsch^ 
takes  a  high  place. 

There  are  several  reasons  why  the  embryological 
method  has  not  in  fact  been  more  fruitful  of 
generalizations  of  value  in  genetics.  The  first, 
and  most  serious,  is  the  infrequence  with  which 
the  working  embryologist  has  had  any  real  or 
deep  appreciation  of  the  relation  of  the  problem 

*  Cf .  for  example  this  author's  recent  paper  "  Der  Vererbungs- 
mechanismus  der  Form."  Arch.  J.  Ent.  Mech.,  Bd.  39,  pp.  516-578, 
1914. 


A  CRITICAL  EXAMINATION  37 

of  somatogenesis  to  the  problem  of  heredity.  He 
has  been  interested  in  other  things.  The  second 
is  that  in  the  main  he  has  worked  with  material 
of  whose  genetic  history  nothing  was  known. 
His  material  was  "impedigreed"  material.  The 
third  is  that  embryology  has  generally  studied  only 
one  part,  the  beginning,  of  somatogenesis.  Post- 
embryonic  development  has  been  regarded  as 
unworthy  of  consideration.  Yet  in  the  main  it  is 
with  adult  characters  that  the  geneticist  deals. 

These  seem  to  be  the  more  important  practical 
reasons  why  embryology  has  not  hitherto  been 
conspicuously  illuminating  as  a  mode  of  genetic 
research.  Logically  considered  this  method  finds 
its  chief  limitation,  like  each  of  the  other  three 
methods,  in  that  it  takes  hereditary  specificities 
as  things  given,  and  makes  no  attempt,  because  it 
has  no  means  of  accomplishing  such  an  end,  to 
investigate  their  origin  or  determination. 

From  the  methodological  standpoint  a  sharp 
distinction  must,  of  course,  be  made  between  the 
older  purely  descriptive  embryology  and  the  mod- 
ern experimental  embryology.  It  is  the  latter 
which  is  of  the  greatest  potential  value  as  a  mode 
of  research  in  genetics.  The  former  (descriptive 
embryology)  is  subject  to  a  considerable  degree 
to  the  same  practical  limitation  as  cytology, 
namely  it  is  essentially  a  static  method.  It  is 
clear,  however,  that  in  experimental  embryology, 
using  the  term  in  the  widest  sense  to  include  the 


38    MODES  OF  RESEARCH  IN  GENETICS 

study  of  such  phenomena  as  regeneration,  regula- 
tion, growth,  etc.,  we  have  a  first-class  tool  for 
the  analysis  of  the  principles  of  somatogenesis. 

It  is  unquestionable  that  a  splendid  opportunity 
lies  open  for  research  in  genetics  by  the  embryo- 
logical  method,  using  the  term  in  the  broad  sense 
just  mentioned.  It  is  altogether  usual  in  current 
discussions  of  variation  and  heredity  to  neglect 
completely  everything  which  comes  between  the 
two  end  terms  of  the  ontogenetic  series,  the  germ 
cell  on  the  one  hand  and  the  adult  soma  on  the 
other  hand.  But  clearly  what  goes  between  is  a 
most  essential  part  of  heredity  itself.  It  is  aston- 
ishing how  little  has  been  done  on  these  extremely 
obvious  problems.  Dr.  Boring  and  the  writer  ^ 
have  recently  undertaken  a  study  of  the  regenera- 
tion of  certain  organs  in  heterozygous  animals, 
to  see  what  is  the  behavior  of  the  successive  re- 
generation in  respect  of  the  character  for  which 
the  individual  is  heterozygous.  Some  of  the 
results,  as  yet  unpublished,  are  very  interesting. 
For  example,  to  mention  but  a  single  case,  we  find 
that  an  individual,  heterozygous  for  plumage 
pattern,  may  from  the  same  feather  follicle  at  one 
time  produce  a  feather  having  a  pattern  like 
that  of  one  of  the  parents,  and  at  another  time  a 
feather  with  a  pattern  like  that  characteristic  of 

1  Cf.  for  a  preliminary  report  of  some  of  these  experiments,  Pearl, 
R.  and  Boring,  A.  M.  "  Some  Physiological  Observations  regarding 
Plumage  Patterns."  Science,  N.  S.,  Vol.  39,  pp.  143-144,  1914. 


A  CRITICAL  EXAMINATION  39 

the  other  parent.  Studies  of  this  sort  are  bound 
to  throw  hght  on  the  puzzling  —  and  too  much 
neglected  —  problem  of  dominance. 

III.   Conclusion 

In  what  has  preceded  we  have  attempted  a 
critical  analysis  of  the  four  general  methods  which 
have  been  employed  in  the  investigation  of  the 
problem  of  heredity.  Two  of  these  methods  have 
been  seen  to  be  essentially  statistical,  and  two 
essentially  biological.  The  statistical  methods  — 
the  biometric  and  the  Mendelian  —  differ  funda- 
mentally only  in  that  the  former  investigates 
primarily  the  ancestry  and  the  latter  primarily  the 
progeny.  Logically  exactly  the  same  distinction 
was  found  between  the  two  purely  biological 
methods  —  the  cytological  and  the  embryologi- 
cal.  The  former  studies  the  ancestry  of  the  germ 
cell  (gametogenesis) ,  the  latter  the  progeny  of 
the  germ  cell  (somatogenesis). 

All  of  these  methods  are  valuable,  and  each 
has  contributed  to  our  present  knowledge  of 
heredity.  No  one  of  the  methods  alone  can, 
however,  solve  the  problem.  They  all  have  at 
least  one  fundamental  limitation  in  common. 
This  is  that  they  offer  no  means  of  directly  getting 
at  any  definite  information  regarding  the  origin, 
cause,  or  real  nature  of  that  specificity  of  living 
material  which  is  the  very  foundation  of  the  phe- 


40    MODES  OF  RESEARCH  IN  GENETICS 

nomenon  of  heredity.  The  distribution  of  heredi- 
tary specificities,  their  putative  morphological 
"bearers,"  and  many  other  things  about  them 
have  been  studied  more  or  less  exhaustively.  The 
things  themselves  have  been  speculated  about,  but 
not  investigated  to  any  but  the  slightest  extent. 

It  is,  however,  plain,  I  think,  what  must  be 
the  mode  of  attack  on  this  outstanding  problem  of 
genetics.  In  the  present  state  of  knowledge  it  is 
beyond  dispute  that  the  basis  of  the  specificity 
of  living  substances  lies  in  its  chemistry.  This 
plain  fact  has  long  been  recognized  by  biologists, 
but  until  very  recently  this  recognition  has  been 
equivalent  practically  to  an  Ignorahimus.  The 
obvious  complexity  of  the  chemical  processes 
going  on  in  living  material  has  made  any  direct 
investigation  of  the  problem  from  this  side  seem 
hopeless  to  the  biologist.  But  this  period  of 
despairing  wonderment  is  passing,  and  that 
rapidly.  The  remarkable  development  of  bio- 
chemistry in  the  last  twenty  years  has  put  at  the 
disposal  of  the  geneticist  a  new  technical  equip- 
ment with  which  he  may  directly  attack  problems 
which  formerly  seemed  impossible  of  approach. 
To  mention  but  a  single  instance  by  way  of  illus- 
tration, the  science  of  serology,  which  has  so  far 
been  developed  almost  exclusively  as  an  adjunct  to 
medicine,  puts  into  the  hands  of  the  biologist  a 
technique  of  enormous  possibilities  in  solving  the 
most  fundamental  problem  of  genetics. 


A  CRITICAL  EXAMINATION  41 

We  have  in  the  past  not  lacked  chemical  theories 
of  heredity.  One  has  but  to  mention  the  names 
of  Pfluger,  Verworn,  Hatschek,  Kossel,  Adami, 
Guyer,  and  many  others  to  recall  such  theories  to 
mind.  The  difficulty,  it  would  seem,  under  which 
all  such  theories  have  labored  is  that,  in  the  ab- 
sence of  the  developed  biochemical  technique  now 
available,  these  theories  have  not  been  framed  on  a 
practical  basis ;  that  is,  they  have  lacked  the 
very  essential  property  of  being  capable  of  direct 
experimental  test.  The  time  seems  now  ripe  for 
a  biochemical  theory  of  the  hereditary  process, 
which  in  the  light  of  our  present  knowledge  and 
technical  equipment  in  the  fields  of  statistical 
mathematics,  experimental  breeding,  cytology, 
and  biochemistry,  shall  be  adapted  to  experi- 
mental verification  or  disproof  as  the  case  may  be. 

Finally,  if,  as  I  fear  may  be  the  case,  I  have 
wearied  the  reader  unduly  with  this  discussion  of 
methods,  instead  of  conducting  him  on  a  journey 
into  the  more  exciting  field  of  results,  my  apologia 
must  be  that,  however  irksome  and  disagreeable 
the  task,  an  occasional  examination  and  overhaul- 
ing of  one's  equipment  is  as  essential  to  success 
in  scientific  operations  as  it  is  in  military.  The 
geneticist's  working  equipment  is  a  good  one,  and 
has  wrought  well.  I  hope  it  has  done  no  harm 
to  try  to  see  just  what  the  limitations  are  to  the 
usefulness  of  each  tool  in  the  list. 


CHAPTER  II 

BIOMETRIC   IDEAS  AND   METHODS  IN  BIOLOGY 
THEIR  SIGNIFICANCE  AND  LIMITATIONS  ^ 


The  last  twenty  years  have  witnessed  the  origin 
and  development  of  what  amounts  to  a  new  branch 
of  biological  inquiry;  namely,  biometry.  This 
subdivision  of  biological  science,  which  has  within 
this  period  come  to  be  practically  a  distinct  and 
separate  Fach,  may  fairly  be  said  to  have  taken  its 
origin  at  about  the  year  1895  in  the  pioneer  in- 
vestigations of  Pearson  and  Weldon.  In  making 
this  statement  there  is  no  implication  that  there 
had  not  been  important  quantitative  work  in 
biology,  of  one  kind  or  another,  before  1895.  There 
certainly  had  been  a  considerable  amount  of  such 
work.  It  had,  however,  fallen  in  special  and 
rather  restricted  fields.  Most  important  in  this 
earlier  quantitative  biology  are  probably  to  be 
reckoned  the  studies  of  the  anthropologists.  In 
this  field  the  work  of  Quetelet  and  of  Galton 
stands  preeminent.  The  work  of  these  men,  and 
in  particular  that  of   Galton,   indeed   served  in 

1  This  paper,  in  somewhat  modified  form,  was  first  published  in 
Scientia,  Vol.  X,  1911. 

42 


BIOMETRIC  IDEAS  AND   METHODS      43 

considerable  degree  as  the  stimulus  for  an  exten- 
sion of  quantitative  ideas  and  methods  into  other 
and  broader  fields  of  biology. 

Nor  was  physical  anthropology  the  only  phase 
of  biology  which  had  been  definitely  cultivated 
along  quantitative  lines  before  1895.  Certain 
branches  of  physiology  have  long  been  highly 
developed  in  this  direction.  One  thinks  par- 
ticularly in  this  connection  of  the  study  of  the 
physiology  of  nerve  and  muscle.  It  is  probably 
no  exaggeration  to  say  that  so  complete  and 
detailed  a  knowledge  of  the  quantitative  as  well 
as  qualitative  relations  of  the  phenomena  in- 
volved as  we  possess  for  nerve-muscle  physiology 
does  not  exist  to-day  in  any  other  branch  of 
biology. 

But  both  in  anthropology  and  physiology  quan- 
titative methods  of  work  were  only  an  incident. 
In  many  cases,  as  we  can  now  see,  the  mathemati- 
cal methods  used  were  inadequate,  or  incorrect. 
Until  Pearson,  following  the  pioneer  investiga- 
tions of  Galton,  began  his  work  no  one  had  ever 
made  any  consistent  and  systematic  attempt 
to  develop  a  special  calculus  directly  adapted  to 
the  discussion  and  analysis  of  biological  data. 
Because  he  did  just  this  thing  Karl  Pearson  will 
stand  as  the  founder  of  biometry  as  a  definite 
technical  subdivision  of  the  science  of  biology. 

The  publication  of  the  earlier  memoirs  in  Pear- 
son's fundamental  series  of  Mathematical  Contri- 


44    MODES  OF  RESEARCH  IN   GENETICS 

hutions  to  the  Theory  of  Evolution  in  the  period 
from  1895  to  1900  excited  much  interest  among 
biologists  all  over  the  world.  The  possibilities 
opened  out  by  these  new  methods  of  research  were 
quickly  noted,  and  served  as  a  stimulus  to  start  a 
number  of  workers  off  on  the  new  paths.  The 
growth  of  interest  and  the  accumulation  of  re- 
sults on  the  subject  were  such  as  to  necessitate  the 
launching  of  a  new  journal,  Biometrika  (now  in  its 
tenth  volume),  devoted  entirely  to  the  publication 
of  researches  in  this  field.  Thus,  biometry  started 
on  its  career  as  an  independent  twig  of  the  bio- 
logical tree  with  a  very  vigorous  and  apparently 
healthy  initial  growth. 

Events  proved,  however,  that  much  of  this 
growth  was  not  by  any  means  of  a  healthy  charac- 
ter. A  very  decided  reactionary  feeling  on  the 
part  of  biologists  regarding  biometry  began  to 
make  itself  felt.  In  place  of  the  enthusiasm  with 
which  efforts  toward  a  quantitative  biology  were 
at  first  received,  an  intensely  critical  and  in  some 
cases  distinctly  hostile  attitude  appeared.  Stu- 
dents were  advised  to  have  nothing  whatever  to  do 
with  this  iniquitous  biometry.  It  was  felt  that 
biometrical  literature  could  safely  be,  and  to  a 
large  extent  was,  disregarded  by  the  general 
biologist. 

The  reasons  for  the  development  of  this  reac- 
tionary attitude  are  now,  I  think,  tolerably  clear. 
The  first  and  most  important  was  that  biologists 


BIOMETRIC   IDEAS  AND   METHODS      45 

very  generally  misunderstood  the  significance 
and  possibilities  of  biometric  methods  as  applied 
to  their  subject.  At  the  outstart  the  enthusiasm 
of  the  biometric  workers  led  to  great  expectations 
as  to  what  the  new  science  was  going  to  accom- 
plish. Because  these  expectations  were  in  large 
degree  based  on  an  entire  misconception  of  what 
mathematical  methods  could  by  any  possibility  do, 
they  were  not  fulfilled,  and  this  naturally  led  to 
more  or  less  of  a  feeling  of  aversion  to  the  whole 
subject.  Such  a  result  would  have  been  inevitable 
whatever  the  quality  of  the  biometric  research 
done. 

In  the  second  place,  biometry  was,  for  some 
time,  taken  to  be  a  school  of  biological  philoso- 
phy rather  than  what  it  really  is,  a  method 
of  research.  The  great  activity  of  biologists 
during  recent  years  in  the  analytical  study  of 
inheritance  by  the  method  of  experimental  breed- 
ing has  served  to  establish  on  a  firm  basis  certain 
fundamental  principles  of  the  physiology  of  the 
hereditary  process  (the  principles  of  segregation, 
and  of  the  normal  stability  of  homozygous  strains). 
It  is  further  the  fact  that  certain  views  regarding 
the  method  of  evolution  and  of  inheritance  in 
plants  and  animals  which  have  been  upheld  by 
certain  leading  biometrical  authorities  are,  in 
regard  to  some  fundamental  points,  utterly  at  vari- 
ance with  the  results  of  these  experimental  investi- 
gations.    By  a  regrettable  confusion  of  thought. 


46    MODES  OF  RESEARCH  IN  GENETICS 

biometry  has  been  arraigned  for  the  views  on 
purely  biological  topics  held  by  certain  individuals. 
Surely  the  application  of  appropriate  mathemati- 
cal methods  to  aid  in  the  solution  of  biological 
problems  involves  per  se  the  maintenance  of  no 
particular  theoretical  position  whatever  with 
regard  to  the  fundamental  nature  of  biological 
processes  or  phenomena. 

In  the  third  place,  it  must  be  admitted  that  a 
good  deal  of  the  early  work  in  biometry  was  of  a 
superficial  character,  and  made  no  contribution 
of  moment  either  to  biology  or  to  biometric 
theory  or  practice.  On  account  of  the  novelty 
of  the  view  point  an  inexhaustible  wealth  of  ma- 
terial lay  ready  to  the  hand  of  the  biometrician. 
If  a  knowledge  of  the  statistical  facts  of  variation  in 
organism  A  was  a  good  thing  to  have,  a  similar 
knowledge  for  B  ought  also  to  be  a  good  thing. 
Nothing  could  be  simpler  than  to  collect  a  lot  of 
individuals,  measure  or  count  something,  and  then 
write  a  paper  setting  forth  the  results  of  this 
activity.  Too  often  the  enthusiasts  who  rushed 
into  the  new  line  of  work  seemed  to  expect  the 
application  of  quantitative  methods  not  only  to 
solve  problems,  but  also  to  furnish  problems 
ready  made. 

Biometry  has  now  safely  passed  that  stage  in 
development,  which  every  new  line  of  investiga- 
tion passes  through  sooner  or  later,  in  which  it 
suffers  at  the  hands  of  its  overzealous  friends.     It 


BIOMETRIC   IDEAS  AND  METHODS      47 

is  gradually  coming  to  be  clearly  recognized  by 
general  biologists  that  biometric  methods  when 
properly  used  add  an  important  weapon  of  re- 
search to  the  investigator's  armament.  It  is  the 
purpose  of  this  paper  to  attempt  in  a  very  modest 
way  to  help  along,  if  possible,  this  better  under- 
standing of  and  greater  sympathy  towards  bio- 
metric work. 

II 

The  underlying  and  essential  point  of  view  of 
biometry  has  been  quite  generally  misunderstood  by 
biologists.  In  the  first  place  biometry  is  often 
sjtrongly  and  quite  unjustly  criticized  because  it  has 
developed  primarily  as  a  statistical  science.  It  is 
supposed  that  this  method  of  inquiry  cannot  prop- 
erly or  profitably  have  anything  to  do  with  any 
problems  not  immediately  reducible  to  frequency 
polygons  and  correlation  tables.  The  charge  is 
made  that  biometrical  methods  can  deal  only  with 
mass  phenomena,  and  that  they  intentionally  disre- 
gard the  detailed  study  of  the  individual,  and 
therefore  lead  directly  to  experimental  indeter- 
minism  as  a  mode  of  biological  thought.  Such 
a  charge  is  based  on  an  entire  misconception  of 
the  biometrical  standpoint.  This  attitude,  how- 
ever, has  done  a  great  deal  of  harm  in  hindering 
the  wider  use  of  these  methods  by  biologists. 
Nothing  has  been  more  strongly  emphasized  by 
the  trend  of  recent  biological  discovery  than  the 


48    MODES  OF  RESEARCH  IN  GENETICS 

importance  of  the  thorough,  searching  study  of 
the  individual,  whether  the  matter  under  inves- 
tigation be  behavior,  inheritance.  Variation,  or 
morphogenesis.  It  is  no  recommendation  for  a 
new  hne  of  scientific  inquiry  to  be  supposed  to 
ignore  or  belittle  this  fact. 

A  second  misconception  which  prevails  rather 
widely  is  to  the  effect  that  biometric  methods, 
being  supposedly  entirely  statistical  in  character, 
necessarily  require  as  a  working  postulate  at  the 
outstart  that  the  accumulation  by  selection  of 
small  fluctuating  variations  is  the  primary  and 
fundamental,  if  not  the  sole  method  of  organic 
evolution.  Such  an  idea  is,  of  course,  absurd. 
The  purpose  of  biometrical  study  so  far  as  it  is 
applied  to  the  evolution  problem  is  precisely  to 
find  out  what  has  been  the  method  of  evolution. 
Whatever  the  results  of  such  inquiry  may  turn  out 
to  be  has  no  relation  to  either  the  validity  or  use- 
fulness of  biometric  methods  per  se.  The  statisti- 
cal methods  or  calculus  developed  by  Pearson 
are  particularly  adapted  to  the  study  of  variation 
of  the  continuous  fluctuating  type,  but  one  who 
uses  this  calculus  is  in  no  way  compelled  because 
of  this  fact  to  take  any  particular  position  in  re- 
gard to  the  theoretical  question  of  the  biological 
importance  or  significance  of  this  kind  of  variation 
in  evolution.  This  is  a  matter  to  be  settled  by 
direct  experiment  and  observation.  If,  as  many 
biologists   are  coming  to   believe,    this    type    of 


BIOMETRIC   IDEAS  AND   METHODS      49 

variation  has,  in  a  strict  sense,  very  little  if  any 
significance  in  evolution,  biometric  methods  will 
help  to  demonstrate  the  fact.  Further,  as  has 
been  implied  above,  the  statistical  study  of 
variation  is  only  one  side  of  biometry. 

Based  on  a  misconception  similar  to  that  just 
discussed  is  the  point  of  view  which  criticizes 
biometry  as  being  necessarily  tied  fast  to  a  par- 
ticular view  regarding  the  hereditary  process. 
The  "law  of  ancestral  inheritance"  first  enunciated 
by  Galton  and  later  extensively  developed  by 
Pearson  is  simply  a  statistical  statement.  It 
concerns  itself  with  the  end  results  of  the  action 
in  a  general  population  of  a  whole  complex  of 
biological  processes,  of  which  inheritance  is  only 
one.  It  is  the  opinion  of  many  workers  in  the 
field  of  genetics  that  this  "law"  probably 
has  very  little  direct  relation  to  the  really  signif- 
icant biological  facts  of  heredity,  and  that 
whatever  apparent  significance  it  may  have  is 
largely  accidental  and  fortuitous.  But  whether 
this  opinion  is  correct  or  not  certainly  has  no  bear- 
ing on  the  question  of  the  validity  of  bringing 
appropriate  and  correct  mathematical  methods  to 
the  aid  of  the  investigator  wherever  they  can  be 
of  help  in  solving  problems.  It  is  a  confusion  of 
thought  to  criticize  a  scientific  method  of  investi- 
gation because  of  the  theoretical  views  held  by 
some  of  those  who  employ  it.  There  is  yet  to 
be  discovered  a  scientific  method  which  can  be 

E 


50    MODES  OF  RESEARCH  IN  GENETICS 

depended  upon  to  give  correct  results  invariably, 
regardless  of  how  it  is  handled  or  applied.  Biom- 
etry is  no  worse  off  in  this  regard  than  is  the  ex- 
perimental method,  the  position  of  which  in  biolog- 
ical methodology  is  now  so  secure. 

The  real  purpose  of  biometry  is  the  general 
quantification  of  biology.  Its  fundamental  view- 
point is  that  without  a  study  of  the  quantitative 
relations  of  biological  phenomena  in  the  widest 
sense  it  will  never  be  possible  to  arrive  at  a  full  and 
adequate  knowledge  of  those  phenomena.  This 
viewpoint  insists  that  a  description  which  says 
nothing  about  the  magnitude  of  the  thing  described 
is  not  complete  but,  on  the  contrary,  lacks  an 
element  of  primary  importance.  It  insists,  also, 
that  an  experiment  which  takes  no  account  of 
the  "probable  error"  of  the  results  reached  is 
inadequate  and  as  likely  as  not  to  lead  to  incorrect 
conclusions.  Further,  and  more  broadly,  it  is 
certain  that  not  only  are  quantitative  methods 
needed  in  biology,  but  also  that  a  far  more  serious 
need  is  for  something  of  the  methodological  view- 
point —  the  mode  of  thinking  —  which  is  charac- 
teristic of  the  exact  sciences.  What  the  writer 
conceives  to  be  the  true  and  basic  standpoint  of 
biometry  cannot  be  better  expressed  than  in  the 
following  remarks  of  that  master  of  an  exact 
physical  science,  Lord  Kelvin,  in  an  address  on 
Electrical  Units  of  Measurement}     *'I  often  say 

*  "Popular  Lectures  and  Addresses,"  Vol.  I,  p.  73. 


BIOMETRIC  IDEAS  AND  METHODS      51 

that  when  you  can  measure  what  you  are  speaking 
about  and  express  it  in  numbers,  you  know  some- 
thing about  it,  but  when  you  cannot  measure  it, 
when  you  cannot  express  it  in  numbers,  your 
knowledge  is  of  a  meager  and  unsatisfactory  kind ; 
it  may  be  the  beginning  of  knowledge,  but  you 
have  scarcely  in  your  thoughts,  advanced  to  the 
stage  of  science,  whatever  the  matter  may  be."      • 

Having  taken  this  position,  the  next  thing  in 
order  obviously  is  to  develop  mathematical 
methods  especially  adapted  to  the  treatment  of 
biological  data.  Such  a  step  is  no  more  to  be 
criticized  than  is  the  demand  of  the  experimentalist 
that  he  shall  have  apparatus  adapted  to  his  needs, 
or  of  the  morphologist  that  he  shall  have  the 
latest  and  best  type  of  microscope  for  his  most 
detailed  and  important  researches.  It  is  the  most 
obvious  right  of  an  investigator  that  he  shall 
have  highly  developed  and  adapted  technical 
aids  whatever  his  field  of  work.  In  accord  with 
this  principle  there  has  been  developed  (partly  by 
borrowing  from  pure  mathematics  and  partly 
de  novo)  a  very  ejQScient  and  tolerably  complete 
system  of  special  mathematical  methods  partic- 
ularly adapted  to  the  analysis  of  quantitative 
biological  data. 

Unfortunately  the  more  recondite  of  these 
methods  cannot  be  understood  at  all  by  the 
general  biologist  unless  a  considerable  amount  of 
careful   and   thorough   study   is   given   to   them. 


52    MODES  OF  RESEARCH  IN  GENETICS 

Even  the  simpler  of  current  biometric  methods  are 
not  fully  understood  by  the  majority  of  biologists, 
nor  can  they  except  through  special  study  of  their 
mathematical  origin  and  development.  But  is 
there  any  reason  why  the  biologist  should  expect  to 
have  intuitive  comprehension  of  these  methods  ? 
No  one  would  expect  to  apply  successfully  the 
complicated  and  delicate  surgical  technique  of 
Pawlow  or  Carrel  to  the  solution  of  biological 
problems  without  careful  preliminary  study  and 
practice  of  these  methods,  continued  till  they 
were  really  mastered.  The  case  is  not  different 
with  any  other  higher  development  of  scientific 
technique. 

Because  of  the  lack  of  a  full  comprehension  of 
the  meaning  and  significance  of  the  mathematico- 
statistical  methods  used  in  biometry,  these 
methods  have  been  subjected  to  a  great  deal  of 
unreasonable  and  futile  criticism.  It  is  argued 
that  these  methods  are  in  large  part  worthless 
because  they  are  too  refined.  Biological  data 
are  held  to  be  of  so  coarse  and  inaccurate  a 
character  as  to  make  any  but  the  roughest  kind 
of  treatment  of  them  of  no  significance.  Such  a 
view  misses  entirely  the  purpose  and  meaning 
of  the  biometrical  calculus.  It  is  just  because 
biological  data  necessarily  are  often  rough  that  we 
need  refined  mathematical  methods  in  their  treat- 
ment in  order  to  test  and  check  the  conclusions 
to  be  drawn  from  them,  and  in  order  to  show  their 


BIOMETRIC   IDEAS  AND   METHODS      53 

true  trend  and  significance.  An  example  will 
help  to  make  the  point  here  clear.  Mortality 
statistics  are  usually  available  only  in  units  of 
years  of  life.  This  is  a  rough  unit.  For  actuarial 
purposes  it  is  desirable  to  know,  for  example,  the 
probable  duration  of  life  much  more  accurately 
than  in  terms  of  years.  It  is  possible  to  get  this 
information,  accurate  to  a  very  high  degree,  by 
the  application  of  appropriate  mathematical  treat- 
ment to  the  rough  yearly  data.  In  this  connec- 
tion, too,  is  to  be  considered  the  frequently  made 
statement  that  no  statistical  constant  can  be  more 
accurate  than  the  data  on  which  it  is  based.  It  is 
very  easy  to  demonstrate  that  this  is  not  true.^ 

While,  as  has  been  pointed  out  in  this  section, 
the  methods  and  point  of  view  of  biometry  have 
not  always  been  understood,  yet  the  indications 
are  that  matters  are  improving  very  rapidly  in 
this  respect.  In  particular  the  great  interest  and 
activity  now  being  displayed  in  the  study  of  in- 
heritance and  plant  and  animal  breeding  is  doing 
much  to  increase  the  use  of  biometric  methods. 
Breeders  are  accumulating  masses  of  data  which 
they  wish  to  analyze.  To  do  this  necessitates  in 
many  cases  the  use  of  biometric  methods.  As 
the  really  purposeful  employment  of  these  methods 
to  help  solve  practical  problems  increases  they 
must  inevitably  come  to  be  better  understood  by 
the  great  mass  of  biologists. 

1  Cf.  Pearl,  R.     Amer.  Nat.,  Vol.  XLIII,  pp.  238-240,  1909. 


54    MODES  OF  RESEARCH  IN  GENETICS 

III 

Let  us  now  turn  to  a  consideration  of  some  of  the 
ways  in  which  biometrical  methods  may  be  of 
immediate  value  to  the  progress  of  biology. 
What  has  biometry  to  offer  to  biology  that  is 
useful?  Or,  in  other  words,  what  is  the  signifi- 
cance of  biometry  ? 

Stated  most  broadly  it  may  be  said  that  biom- 
etry brings  to  biology  a  fairly  well  developed 
method  or  system  for  the  more  precise,  accurate, 
and  complete  description  of  biological  phenomena. 
Biometry  is,  in  last  analysis,  a  descriptive  method. 
Like  all  other  descriptive  methods,  or  phases  of 
science,  it  is  not  likely  in  and  by  itself  ever  to 
solve  completely  any  problems.  It  must  always 
work  in  conjunction  with  the  experimental  method 
to  attain  the  highest  {i.e.,  most  valuable)  type  of 
results.  But  at  the  same  time  it  brings  to  the 
aid  of  the  experimentalist  that  which  is  of  the  ut- 
most importance ;  namely,  an  adequate  method  of 
describing,  analyzing,  and  in  general  reaching 
correct  conclusions  from  the  results  of  experimenta- 
tion. 

Biometry  affords  an  extension  of  descriptive 
methods  in  a  direction  where  such  an  extension  is 
often  an  absolute  requisite  of  truly  scientific  work, 
and  in  a  direction  where  no  other  method  is  avail- 
able. Ordinary  biological  observation  and  de- 
scription has  as  its  unit  the  individual,  or  some  part 


BIOMETRIC  IDEAS  AND   METHODS      55 

of  the  individual.  It  describes  the  individual  in 
terms  of  its  own  qualities  or  attributes.  If  an 
adequate  description  of  the  individual  is  given,  it 
does  not  concern  itself  solely  with  the  separate 
parts,  but  discusses  the  qualities  and  attributes 
of  the  individual  as  a  whole.  Thus  it  would  not 
be  an  adequate  description  of  a  man  to  say  that  he 
was  the  sum  of  such  and  such  bones,  muscles, 
nerves,  and  blood  vessels.  A  cat  possesses  much 
the  same  bones,  muscles,  nerves,  and  blood  vessels 
that  a  man  has.  It  is  probably  no  exaggeration 
to  say  that  the  similarity  between  man  and  cats 
in  respect  to  these  organ  systems  is  so  great  that 
a  person  without  previous  experience  of  either  — 
say  a  Martian  —  unless  he  were  deeply  versed 
in  anatomy,  might  very  possibly  consider  cats 
to  be  dwarf  men  if  he  had  as  a  basis  of  distinction 
only  a  formal  description  of  the  organ  systems 
named.  Any  adequate  description  of  an  organism 
must  include  as  its  most  fundamental  and  im- 
portant part  an  account  of  the  attributes  and 
qualities  of  that  organism  as  a  whole. ^ 

Now  a  little  consideration  will  serve  to  convince 
one  that  the  ordinary  methods  of  description  as 
used  in  biology  fail  {i.e.,  become  altogether  inade- 
quate) when  the  attempt  is  made  to  deal  with  any 
group  of  individuals,  as  for  example  a  population, 

^  This  point  has  been  developed  in  a  masterly  way  in  a  paper 
by  Professor  William  E,  Ritter,  having  the  title  "Life  from  the 
Biologist's  Standpoint"  in  Popular  Science  Monthly,  August,  1909. 


56    MODES  OF  RESEARCH  IN  GENETICS 

race,  variety,  species,  or  larger  group.  These 
methods  fail  because  they  are  fundamentally 
and  necessarily  incapable  of  giving  a  description 
of  the  group  (whatever  its  magnitude)  in  terms 
of  anything  but  the  individuals  which  compose  it. 
That  is  to  say,  they  have  no  way  of  getting  at  a 
description  of  a  group  {e.g.,  a  species)  as  a  whole  or 
as  such,  in  terms  of  its  (the  group's)  attributes 
and  qualities.  Let  an  illustration  make  this 
point  clear.  The  purpose  of  systematic  zoology 
is  to  classify  and  arrange  animals  in  natural 
groups.  As  a  necessary  step  in  the  carrying  out 
of  this  purpose  it  is  obliged  to  attempt  to  define, 
which  means  describe,  these  groups.  But  its 
whole  way  of  going  about  this  process  is  a  con- 
fession of  the  fundamental  inadequacy  of  the 
method.  The  systematist  frankly  makes  no  at- 
tempt whatever  to  describe  or  define  a  particular 
species  as  a  species  {i.e.,  as  a  group  of  animals) 
in  terms  of  its  (the  species')  qualities.  Instead 
he  describes  one  individual  animal  belonging  to 
this  species ;  affirms  either  expressly  or  tacitly 
that  all  other  individuals  belonging  to  the  species 
are  "about"  or  "generally"  like  the  individual 
described,  and  then  calls  the  net  result  the  defi- 
nition or  description  of  the  species.  But  now 
surely  this  is  not  a  description  of  the  species  at 
all.  An  adequate  description  of  the  species  will 
be  one  which  takes  account  of  its  peculiarities  as 
a  unit,  and  indicates  how  it  as  a  unit  or  as  a  whole 


BIOMETRIC   IDEAS  AND   METHODS      57 

is  distinguished  from  other  similar  groups.  In 
making  this  statement  there  is,  of  course,  no  im- 
plication that  the  facts  set  forth  by  the  systematist 
are  not  desirable  and  useful.  But  something  more 
is  needed  to  gain  a  well-rounded,  adequate  idea  of 
the  group,  whether  species,  variety,  or  any  other. 

It  is  a  particular  and  fundamental  point  of 
significance  of  biometry  for  biology  that  it  offers 
an  adequate  solution  of  just  this  problem  of  the 
description  of  the  group  as  a  whole  or  a  unit  in 
terms,  not  of  its  component  individuals,  but  of 
its  own  attributes  and  qualities.  The  biometrical 
constants  (mean,  standard  deviation,  coefficient 
of  variation,  etc.)  are,  within  the  limits  of  error  of 
random  sampling,  constants  characteristic  of  the 
group  as  such,  and  not  of  any  particular  individual 
or  individuals  in  it.  So,  further,  the  shape  of  the 
variation  curve  for  a  particular  group  of  organisms 
is  something  definitely  characteristic  for  the  group. 

The  fact  that  in  statistical  methods  we  have  the 
means  of  accurately  describing  the  attributes  of 
groups  or  organisms  as  groups  affords  an  oppor- 
tunity of  investigating  why  groups  {i.e.,  species, 
varieties,  etc.)  come  to  have  the  characteristics 
which  they  do.  It  is  the  highest  aim  of  the  bio- 
metrical study  of  variation  to  determine  the  bio- 
logical causes  which  underlie  the  formation  of 
the  particular  sort  of  frequency  curves  which 
actually  are  found,  rather  than  some  one  of  the 
innumerable  other  sorts  which  might  conceivably 


58    MODES  OF  RESEARCH  IN  GENETICS 

have  arisen  in  any  individual  instance.  A  first 
study  in  this  direction  was  made  by  the  writer 
for  variation  in  the  plant  Ceratophyllum.^  More 
recently  fundamental  researches  of  a  similar 
character  have  been  made  by  Jennings  on  varia- 
tion in  Paramecium.  In  the  writer's  laboratory 
a  study  has  lately  been  made,  from  this  point  of 
view,  of  the  inter-individual  (racial)  variation 
curves  of  one  of  the  higher  plants. ^  The  first 
necessity  in  all  such  analytical  studies  must  be 
a  precise  description  and  definition  of  the  things 
which  are  to  be  analyzed.  Such  a  description  the 
application  of  biometric  methods  furnishes. 

In  what  has  been  said  regarding  biometry  as 
a  method  of  group  description,  reference  has  been 
made,  for  the  sake  of  simplicity  of  illustration,  to 
groups  of  individual  organisms.  The  same 
considerations,  however,  apply  with  equal  or 
perhaps  ever  greater  force  to  the  study  by  bio- 
metrical  methods  of  groups  of  like  parts  or  organs 
within  the  single  individual.  Appropriate  quan- 
titative methods  make  it  possible  to  detect  and 
analyze  the  most  subtle  phenomena  of  differen- 
tiation in  the  development  and  growth  of  the  in- 
dividual. In  the  absence  of  methods  for  dealing 
with  a  group  of  parts  or  individuals  as  such,  one 

1  Carnegie  Institution  of  Washington,  Publication  No.  58,  1907. 

2  Pearl,  R.  and  Surface,  F.  M.  "Growth  and  Variation  in 
Maize."  Zeitsch.  f.  ind.  AbsL-  u.  Vererbungslehre,  Bd.  XIV,  pp.  97- 
203,  1915. 


BIOMETRIC   IDEAS  AND  METHODS      59 

would  be  quite  unable  to  attack  a  whole  series  of 
interesting  and  fundamental  problems  of  mor- 
phogenesis. Such  problems,  for  example,  as  the 
precision  of  morphogenetic  localization,  or  the 
degree  of  variability  of  successively  regenerated 
structures  (does  the  morphogenetic  mechanism 
learn  to  work  better  with  practice?),  or  the  exist- 
ence and  nature  of  fundamental  laws  of  growth 
determining  the  general  features  of  the  tectonics 
of  large  groups  of  plants  and  animals,  etc.,  demand 
the  application  of  biometric  methods  if  they  are 
to  be  adequately  treated.  There  is  a  host  of 
problems  of  morphogenesis  of  this  general  charac- 
ter as  yet  hardly  touched  at  all  by  the  biologists. 
Biometric  methods  which  enable  us  to  deal  with 
groups  of  things  or  events  as  groups  furnish  the 
key  to  the  successful  attack  on  these  problems. 
Pioneer  work  in  this  direction  is  being  done,  but 
there  is  a  vast  and  fertile  field  here,  the  proper 
cultivation  of  which  will  demand  the  combined 
efforts  of  many  workers.  To  the  application  of 
appropriate  biometric  methods  in  this  field  we 
may  confidently  look,  I  think,  as  the  source  of  a 
significant  advance  in  the  building  up  of  a  science 
of  causal  morphology. 

The  second  fundamental  contribution  of  biom- 
etry to  biology  lies  in  the  fact  that  it  has  shown, 
and  in  the  future  will  still  more  impress  upon  the 
biologist,  the  significance  and  great  importance 
in  all  his  work  of  the   probable   error   concept. 


60    MODES  OF  RESEARCH  IN  GENETICS 

Whatever  the  material  of  scientific  investiga- 
tion, whether  animate  or  inanimate,  it  is  a 
fact  of  universal  experience  that  just  as  soon 
as  observation  or  experiment  concerns  itself  with 
any  quantitative  aspect  of  a  phenomenon  it 
is  impossible  ever  to  get  precisely  the  same 
result  twice.  The  more  refined  and  delicate  the 
instrument,  and  the  finer  the  units  in  which  the 
measurement  is  made,  the  more  evident  does  it 
become  that  the  "absolute"  determination  of 
any  magnitude  whatsoever  is  humanly  impossible. 
The  problem  of  all  quantitative  science,  therefore, 
is  to  determine  with  a  maximum  of  accuracy  the 
probability  that  any  particular  unknowable  magni- 
tude lies  within  any  assigned  limits.  One  never 
can  say,  and  be  scientifically  accurate,  that  a 
particular  stick  is  precisely  11.5  cm.  long,  but  if 
it  be  worth  one's  while,  it  is  possible  to  determine 
the  mathematical  probability  that  the  true  length 
of  the  stick  lies  between  say  11.498  and  11.502 
cm.  In  the  writer's  opinion  it  must  be  regarded 
as  the  point  of  greatest  value  of  statistical  theory 
for  science  in  general  that  it  furnishes  the  method 
of  determining  such  probabilities. 

That  the  probable  error  concept  is  of  high  im- 
portance for  biology  is  so  evident  as  not  to  need 
lengthy  discussion.  When  one  considers  what  a 
large  part  of  the  results  of  experimental  investi- 
gations of  all  kinds  of  physiological  topics  (to 
take  but  one  instance)  are  quantitative  in  charac- 


BIOMETRIC   IDEAS  AND  METHODS      61 

ter,  and  based  on  the  observation  of  relatively 
few  individual  cases,  the  significance  of  probable 
error  determinations  in  that  field  is  clear.  Simi- 
larly, in  the  experimental  study  of  inheritance 
along  Mendelian  lines  the  results,  as  has  been 
pointed  out  in  the  preceding  essay,  are  quantita- 
tive and  statistical  in  character.  A  statement  of 
such  results  without  probable  errors  is  incomplete. 
In  the  third  place  biometry  gives  us  a  method  of 
measuring  the  relationship  between  the  phenom- 
ena, in  the  multitude  of  cases  where  this  rela- 
tionship is  not  of  a  simple  cause  and  effect  sort.  In 
observed  biological  phenomena  there  very  often 
exists  a  correlation  rather  than  a  strictly  causal 
relation  between  events  or  characters.  The  reason 
for  this  doubtless  lies  in  the  fact  that  in  biology 
we  are  dealing  in  most  instances  with  complex 
phenomena.  As  the  complex  phenomena  are  an- 
alyzed into  their  simple  (or,  perhaps  better,  simpler) 
components,  correlation  passes  over  into  causation. 
It  is,  however,  a  great  aid  in  making  such  analyses 
to  have  a  method  of  measuring  exactly  the  degree 
of  correlation  which  exists  between  observed 
phenomena  or  characters.  Of  such  methods 
current  biometrical  technique  furnishes  a  great 
wealth.  It  is  possible  now  to  determine  the  de- 
gree of  correlation  or  association  existing  not  only 
between  physically  measurable  characters,  but 
also  between  qualitative  characters  not  capable  of 
precise  measurement. 


62    MODES  OF  RESEARCH  IN  GENETICS 

IV 

Let  us  now  turn  our  attention  to  the  considera- 
tion of  the  limitations  of  biometry  as  a  branch 
of  biological  science.  There  is,  I  think,  funda- 
mentally but  one  such  limitation  of  a  general 
character.  This  arises  out  of  the  fact,  already 
mentioned,  that  biometrical  methods  of  research 
are,  in  last  analysis,  strictly  and  purely  descriptive 
in  character.  There  are  but  two  general  ways  of 
acquiring  and  formulating  a  knowledge  of  nat- 
ural phenomena.  These  are  the  descriptive 
method  on  the  one  hand,  and  the  experimental 
method  on  the  other  hand.  Biometrical  methods 
belong  in  the  first  of  these  categories.  The  only 
thing  which  they  are  able  to  do  is  to  furnish  a 
description,  in  quantitative  terms,  of  existing 
phenomena.  This  does  not,  of  course,  imply 
that  they  are  not  useful  aids  in  experimental 
investigations.  Indeed,  it  is  just  here  that,  in 
the  writer's  opinion,  biometry  finds,  in  general, 
its  highest  usefulness  in  biology.  It  is  only  de- 
sired to  emphasize  the  fact  that  biometric  methods 
are  per  se  purely  descriptive,  and  have  the  limi- 
tations implied  thereby. 

In  actual  biometric  work  the  importance  of 
keeping  clearly  in  mind  the  limitations  and  precise 
significance  of  the  methods  used  is  great.  To 
reach  biologically  significant  results  one  must 
understand  clearly  just  what  is  being  measured 


BIOMETRIC   IDEAS  AND  METHODS      63 

and  what  the  utility  of  that  measurement  really  is. 
Failure  to  do  this  is  bound  to  result  in  confusion 
of  thought.  No  description  has  any  significance 
unless  the  thing  described  has  some  meaning  and 
interest.  Just  here  is  where  so  much  of  the  bio- 
metrical  work  which  has  been  done  has  failed. 
Too  often  has  there  been  an  espousal  of  the  forlorn 
hope  that  the  application  of  biometric  methods 
might  inject  biological  interest  and  meaning 
into  a  problem  previously  quite  destitute  of  these 
attributes. 

Further,  it  is  of  the  highest  importance  for  the 
correct  application  of  biometric  methods  to  under- 
stand thoroughly  the  biological  implications  of 
the  particular  method  employed.  Failure  to 
do  this  is  bound  to  lead  one  into  all  sorts  of  pit- 
falls. It  has  been  a  very  unfortunate  boast  of 
some  biometricians  that  their  methods  involved 
no  biological  assumption  or  implication  whatever. 
Such  a  statement  is  seen  upon  critical  examina- 
tion to  involve  a  logical  difficulty.  Biometric 
methods,  considered  solely  as  pure  mathematical 
reasoning,  certainly  have  no  biological  implica- 
tions, but  the  moment  they  are  applied  to  biological 
data  for  the  solution  of  biological  problems  they  do 
carry  biological  implications.  Otherwise  their 
application  is  altogether  irrational  and  futile.  If 
no  biological  meaning  or  implication  attaches  to 
the  determination  of  the  degree  of  correlation 
between  parent  and  offspring,  for  example,  it  is 


64    MODES  OF  RESEARCH  IN  GENETICS 

evidently  a  waste  of  time  to  calculate  such  cor- 
relations. Further,  if  it  cannot  be  clearly  shown 
that  the  method  of  determining  such  correlations 
is  such  as  to  lead  to  a  biologically  valid  result, 
the  application  of  the  method  in  biology  is 
equally  idle.  As  the  point  here  under  consid- 
eration is  one  of  fundamental  importance,  it 
will  be  well  to  give  it  full  discussion  with  a  con- 
crete illustration. 

It  has  been  frequently  maintained  by  Pearson  ^ 
that  the  *'law  of  ancestral  inheritance,"  which 
states  that  the  correlation  between  offspring  and 
their  ancestors  decreases  in  a  geometrical  progres- 
sion as  the  number  of  included  ancestral  genera- 
tions increases,  involves  no  biological  implication 
whatever  regarding  inheritance.  Further,  it  has 
been  stated  on  the  same  authority  that  the  method 
by  which  this  law  is  deduced  (namely,  by  determin- 
ing the  correlations  which  exist  between  offspring 
and  their  ancestors)  is  valid  whatever  may  be 
the  biological  basis  or  mode  of  inheritance.  Now, 
as  a  matter  of  fact,  practically  all  of  the  work 
which  has  been  done  upon  inheritance  by  Pearson 
and  his  co-workers  seems  to  the  writer  to  involve 
from  its  very  beginning  a  fundamental  biological 
assumption.  This  assumption  is  that  a  correct 
determination  of  the  correlation  in  respect  to 
external,  somatic  characters  between  genetically 
related  individuals,  is  an  adequate  measure  of  the 

^  Cf.  for  example,  Biometrika,  Vol.  II,  p.  217,  1909. 


BIOMETRIC  IDEAS  AND  METHODS      65 

intensity  ^  of  inheritance  between  these  individuals. 
But  the  vaHdity  of  this  assumption  has  never 
been  demonstrated,  and  presumably  never  can 
be,  because  the  assumption  itself  is  contrary  to 
demonstrated  biological  facts,  which  can  at  any 
time  be  experimentally  verified.  The  facts  to 
which  I  allude  are  those  upon  which  rest  the 
demonstration  of  the  existence  of  the  genotype  as 
contrasted  with  the  phoenotype  in  inheritance. ^ 

These  facts  in  general  show  that  the  somatic 
and  the  germinal  conditions  or  states  with  ref- 
erence to  a  particular  character  may  be  quite 
different  in  the  same  individual.  It  results,  then, 
that  the  somatic  condition  of  such  a  character  in 
the  progeny  has  no  direct  or  necessary  relation 
to  the  somatic  condition  of  the  same  character 
in  the  parent. 

Nothing  is  brought  out  more  clearly  by  all 
recent  experimental  studies  of  inheritance  than 
that  the  somatic  condition  of  a  character  in  a 
particular  organism  is  a  very  unreliable  criterion 

1  This  term  "intensity  of  inheritance"  has  been  very  generally 
used  by  biometricians.  One  ventures  to  wonder,  in  the  light  of 
present  knowledge,  whether  the  expression  itself  does  not  involve  an 
unsound  assumption.  As  a  matter  of  fact,  is  inheritance  ever  a 
graded  phenomenon,  as  implied  in  this  expression  ?  The  whole  body 
of  evidence  available  makes  this  seem  to  me  extremely  doubtful. 
However,  I  have  no  desire  at  this  time  to  press,  or  even  to  argue,  the 
point.  I  merely  offer  the  suggestion  that  the  critical  reader  think 
it  over  for  himself. 

2  Cf.  Johannsen,  W.  "Elemente  der  exakten  Erblichkeitslehre," 
3d  edit.,  1913. 

F 


66    MODES  OF  RESEARCH  IN  GENETICS 

of  the  probable  condition  of  that  character  in 
the  progeny  of  that  organism. 

Thus,  to  take  some  concrete  instances  by  way  of 
illustration,  if  one  breeds  a  Cornish  Game  cock 
bird  to  a  Barred  Rock  female,  the  female  offspring 
resulting  will  not  be,  in  respect  to  plumage, 
color  pattern,  in  the  slightest  degree  like  either 
parent.  On  the  contrary  they  will  be  solid  black 
in  color.  1  A  knowledge  of  the  somatic  condition 
of  the  parents,  in  such  a  case,  no  matter  how 
detailed  it  might  be,  would,  in  advance  of  the 
actual  breeding  test,  give  no  clew  whatever  as  to 
the  probable  somatic  condition  of  its  offspring. 
Yet,  in  its  procedure  of  correlating  parent  and 
offspring  in  respect  to  somatic  characters,  the 
"law  of  ancestral  inheritance"  definitely  assumes 
that  the  somatic  condition  of  the  one  may  be 
taken  as  a  valid  and  reliable  criterion  of  the  other. 
Many  cases  like  that  just  cited  might  be  given 
from  existing  Mendelian  literature.  Indeed,  it 
may  be  said  that  nearly  all  experiments  in  crossing 
plants  or  animals  furnish  illustrations  of  the 
general  principle  that  the  somatic  condition  of  a 
character  may  be  a  most  unreliable  criterion  of  its 
probable  behavior  in  inheritance. 

It  may  be  objected  that  the  types  of  cases  cited 
in  the  preceding  paragraph  are  hardly  a  fair  basis 
for  the  criticism  of  the  law  of  ancestral  inheritance 

1  For  details  see  Pearl,  R.,  and  Surface,  F.  M.  Arch.  f.  Ent. 
Mech.y  Bd.  30,  pp.  45-61,  1910.     (Roux  Festschrift.) 


BIOMETRIC  IDEAS  AND  METHODS      67 

in  regard  to  the  logical  foundation  of  the  procedure 
by  which  it  is  deduced,  since  the  illustrations 
mentioned  concern  themselves  with  qualitative 
variations,  whereas  it  is  with  quantitative  varia- 
tions that  the  biometrical  study  of  inheritance 
has  had  to  do.  As  a  matter  of  fact  the  case  for 
the  law  is  made  no  better  if  this  contention  be 
granted,  though  it  is  difficult  to  see  what  reason 
exists  for  supposing  that  so-called  qualitative 
variations  are  not  inherited  in  fundamentally  the 
same  way  as  are  so-called  quantitative  variations. 
Every  character  and  every  variation  has  both  a 
qualitative  and  a  quantitative  aspect.  But  if  we 
consider  only  the  quantitative  aspect  of  the  matter, 
as  has  been  done  in  much  of  the  biometric  work 
on  inheritance,  the  same  principle  of  the  unre- 
liability of  somatic  conditions  as  a  criterion  of 
hereditary  behavior  comes  clearly  forth  from  the 
work  of  Johannsen^  on  beans,  that  of  Jennings  ^ 
on  Paramecium,  investigations  regarding  the  in- 
heritance of  fecundity  in  the  domestic  fowl,^  and 
many  other  recent  studies  along  similar  lines  by 
various  investigators. 

All  of  the  experimental  investigations  referred 
to  agree  in  showing  in  a  most  definite  and  indubi- 
table manner  that  there  exist  two  distinct  cate- 

^  Loc.  cit. 

2  Jennings,  H.  S.  Proc.  Amer.  Phil.  Soc,  Vol.  XL VII,  pp.  393-546, 
1908. 

3  Pearl,  R.    Jour.  Exp.  ZooL,  Vol.  13,  pp.  153-268,  1912. 


68    MODES  OF  RESEARCH  IN  GENETICS 

gories  of  variation,  and  that  this  fact  must  never 
be  lost  sight  of  in  any  discussion  of  heredity  which 
is  to  lead  to  valid  conclusions.  On  the  one  hand 
are  the  variations  which  are  definitely  inherited 
{i.e.,  reappear  in  the  progeny),  presumably  be- 
cause they  are  in  some  way  represented  in  the 
germinal  substance ;  on  the  other  hand  are  the 
purely  somatic  variations  which  do  not  reappear 
in  the  offspring  and  are  not  inherited,  presumably 
because  they  are  not  represented  in  the  germinal 
substance.  Now  the  "law  of  ancestral  inherit- 
ance" entirely  disregards  the  existence  of  these 
two  sorts  of  variations.  In  its  fundamental 
thesis  that  the  correlation  between  parent  and 
offspring  in  regard  to  somatic  conditions  is  a  valid 
measure  of  the  intensity  of  inheritance  it  definitely 
and  implicitly  assumes  that  all  variations  are  of 
equal  significance  in  heredity.  Upon  this  funda- 
mental biological  error,  which  is  taken  as  a  basic 
assumption,  the  whole  superstructure  of  the  bio- 
metric  treatment  of  inheritance  is  reared.  When 
the  significance  and  consequences  of  this  initial 
error  are  perceived  it  is  seen  at  once  that  the  whole 
reasoning,  so  far  as  it  concerns  heredity,  falls  to 
the  ground.  Thus  it  is  assumed  that  the  existence 
of  a  definite  degree  of  correlation  (say  r  =  0.40 
=t  0.02)  between  parent  and  offspring  indicates 
inheritance,  providing  both  generations  have 
been  reared  under  reasonably  the  same  environ- 
mental conditions,  and  an  absence  of  correlation 


BIOMETRIC  IDEAS  AND  METHODS      69 

(r  =  0)  under  similar  circumstances  means  that 
the  character  studied  is  not  inherited.  But  the 
work  of  Johannsen  and  Jennings  indicates  that 
in  general  there  is  no  correlation  (r  =  0)  between 
parent  and  offspring  within  the  genotype  (i.e., 
within  the  same  pure  line).  Are  we  to  conclude 
then  that  there  is  no  inheritance  within  the  geno- 
type —  within  a  group  of  individuals  where  the 
offspring  breed  absolutely  true  generation  after 
generation  ? 

What  a  correlation  coefficient  deduced  from  a 
parent-offspring  correlation  table  which  includes 
a  random  sample  of  parents  in  general,  or  offspring 
in  general,  really  measures,  is  what  may  be  called 
the  orderly  heterogeneity  of  the  material  which 
goes  into  the  table.  One  gets  out  of  the  table  by 
way  of  the  correlation  coefficient  merely  a  measure 
of  what  was  put  into  the  table  as  raw  data.  If 
the  table  includes  individuals  belonging  to  several 
distinct  genotypes,  we  may  expect  to  get  from  it, 
in  many  cases  at  any  rate,  a  sensible  correlation 
coefficient  between  parent  and  offspring.  But 
this  coefficient  does  not  measure  the  intensity  of 
inheritance  between  parent  and  offspring  with 
reference  to  the  character  considered.  It  simply 
measures  the  mutual  interrelation  (as  to  range  and 
distribution  of  variation)  of  the  several  genotypes 
which  went  into  the  table.  The  coefficient 
indicates,  in  other  words,  that  there  are  certain 
groups  of  individuals  within  the  table  which  are 


70    MODES  OF  RESEARCH  IN  GENETICS 

differentiated,  in  respect  to  both  parent  and 
offspring,  from  certain  other  groups  in  the 
same  table.  It  does  not  tell  us  what  the  basis 
of  this  differentiation  is.  It  may  be  inheritance, 
as  it  is  assumed  to  be  in  the  illustration  here  under 
discussion ;  it  may  be  local  environmental  differ- 
ences or  it  may  be  anything  whatever  so  far  as 
the  correlation  method  jper  se  helps  us.  The 
only  way  to  determine  whether  the  "differences" 
indicated  by  the  correlation  method  are  really 
heritable  is  to  apply  the  method  of  individual 
pedigree  analysis  to  the  complex,  heterogeneous 
material  of  the  table.  If  it  is  possible  to  isolate 
and  propagate  distinct  genotypes  from  the  ma- 
terial, then  it  may  be  concluded  that  the  primary 
basis  of  the  differentiation  or  heterogeneity 
detected  by  the  correlation  coefficient  was  in- 
heritance. 

There  can  be,  of  course,  no  valid  objection  to 
the  study,  in  and  for  itself,  of  the  correlation  exist- 
ing between  genetically  related  individuals  in 
respect  of  somatic  characters.  Such  studies  may, 
indeed,  for  one  reason  or  another,  have  a  high  in- 
trinsic interest.  The  point  I  would  emphasize, 
however,  is  that  in  dealing  with  such  correlations 
one  should  always  keep  clearly  in  mind  that  he  is 
not  dealing  directly  and  primarily  with  phenomena 
of  inheritance,  but  only  indirectly  and  secondarily. 

To  summarize  this  discussion,  it  may  be  said 
that  to  attempt  to  draw  conclusions  in  regard  to 


BIOMETRIC  IDEAS  AND  METHODS      71 

inheritance  from  studies  involving  the  correlation 
method  alone  is  futile,  because  the  coefficient 
of  correlation  in  such  studies  can  only  tell  us  of 
the  existence  and  degree  of  an  orderly  differentia- 
tion or  heterogeneity  in  the  material  collected 
together  in  the  correlation  table.  To  determine 
definitely  whether  the  basis  of  the  heterogeneity 
is  inheritance,  recourse  must  be  had  to  pedigree 
analysis  in  terms  of  individuals  and  of  families. 
Of  course  it  will  be  true  in  many  cases  in  actual 
practice  that  general  considerations  make  it  a 
priori  highly  probable  or  even  certain  that  the 
basis  of  an  observed  heterogeneity  is  inheritance. 
In  such  cases  the  coefficient  of  correlation  may 
be  said  to  indicate  the  existence  of  inheritance, 
though  not  to  measure  its  intensity.  But  the 
first  and  fundamental  demonstration  that  a  charac- 
ter is  inherited  in  a  given  group  of  individuals 
must  always  rest  upon  some  other  basis  than 
coefficients  of  correlation  alone.  The  essential 
point  here  made  regarding  the  inherent  difficulty 
in  the  interpretation  of  correlation  coefficients, 
has  been  very  ably  discussed  by  G.  Udny  Yule.^ 
I  am  in  entire  agreement  with  his  position. 

The  general  purpose  of  this  discussion  regarding 
the  study  of  inheritance  has  been  to  show,  by  a 
concrete  example,  how  erroneous  biological  assump- 

^  Yule,  G.  Udny.  "On  the  Interpretation  of  Correlations  be- 
tween Indices  or  Ratios."  Jour.  Roy.  Stat.  Soc,  Vol.  LXXIII,  pp. 
644-647,  1910. 


72    MODES  OF  RESEARCH  IN  GENETICS 

tions  at  the  foundation  may  invalidate  completely 
a  whole  line  of  biometrical  reasoning.  It  is  hoped 
that  this  discussion  will  emphasize  the  importance 
of  the  point  made  at  the  beginning,  that  it  is 
necessary  always  to  keep  clearly  in  mind  the  limi- 
tations of  the  biometric  method  in  general. 
Biometry  furnishes  a  valuable  and  refined  exten- 
sion of  the  descriptive  method.  Its  future  use- 
fulness to  biology  depends  largely  upon  a  clear 
recognition  of  two  things.  These  are,  on  the  one 
hand,  that  biometric  methods  are,  in  their  essential 
nature,  purely  descriptive  methods  of  investiga- 
tion, and,  on  the  other  hand,  that  for  the  valid 
employment  of  these  methods,  it  is  necessary  to 
use  as  much  general  biological  intelligence  in 
regard  to  the  significance  of  the  biological  problem, 
the  biological  validity  of  the  assumptions  made  in 
applying  mathematical  methods  to  the  problem, 
and  the  applicability  of  the  particular  methods 
used  to  the  particular  problem  studied,  as  would 
be  exercised  in  any  investigation  by  any  other 
method. 


CHAPTER  III 
ON  THE  NATURE  OF  STATISTICAL  KNOWLEDGE 


There  is  a  very  general  tendency,  including 
in  its  operation  not  only  the  layman  but  also  the 
professional  man  of  science,  towards  the  notion 
that  there  is  a  special  virtue,  a  sort  of  transcend- 
ent heuristic  worth,  in  such  knowledge  as  is 
reached  by  the  examination  of  large  numbers  of 
cases.  There  seems  to  be  a  feeling,  sometimes 
apparently  almost  mystic  in  its  origin  and  in  its 
strength,  to  the  effect  that  statistical  knowledge 
is  a  higher  and  better  kind  of  knowledge  than 
any  other.  Numberless  quotations  might  be 
cited  to  show  the  prevalence  of  this  view.  Every 
one  has  seen  passing,  as  it  were  in  review,  the  line 
of  problems,  which,  if  we  may  trust  the  assertions 
of  the  interested  individuals,  can  "only  be  solved" 
by  the  application  of  the  statistical  method. 
Evolution,  and  the  factors  of  evolution,  variation, 
heredity,  and  so  on,  are  conspicuously  the  bio- 
logical problems  of  which  this  assertion  has  been 
made. 

Now  this  attitude  towards  statistical  knowledge 
and  statistical  ideas   (which,   of  course,   include 

73 


74    MODES  OF  RESEARCH  IN  GENETICS 

besides  the  compilation  of  large  numbers  of 
individual  instances,  the  concepts  of  averages, 
approximation,  and  probability)  may  be  entirely 
right  and  justifiable.  Indeed,  a  cautious  person 
is  bound  to  be  very  chary  about  even  suggesting 
any  criticism  of  it  when  he  finds  the  following 
statement  made  by  so  distinguished  an  authority 
as  Professor  Royce.^  *'I  am  next  led  to  say  that 
whether  the  natural  world  is  a  mechanism  or  not, 
the  statistical  view  of  nature  would  be,  and  so 
far  as  we  know  the  facts,  is  applicable  to  suflSciently 
complicated  systems  of  things  and  events,  not 
as  mere  substitute  for  those  more  exact  computa- 
tions which  our  ignorance  of  mechanical  laws 
makes  necessary,  but  as  an  expression  of  a  very 
positive,  although  only  probable  and  approximate 
knowledge  whose  type  all  of  the  organic  and 
social  sciences,  as  well  as  most  aspects  of  the 
inorganic  sciences,  illustrate.  There  is,  therefore, 
good  reason  to  say  that  not  the  mechanical  but 
the  statistical  form  is  the  canonical  form  of 
scientific  theory,  and  that  if  we  knew  the  natural 
world  millions  of  times  more  widely  and  minutely 
than  we  do,  the  mortality  tables  and  the  com- 
putations based  upon  a  knowledge  of  averages, 
would  express  our  scientific  knowledge  about 
individual  events,  much  better  than  the  nautical 
almanac  would  do.     For  our  mechanical  theories 

1  Royce,  J.     "The  Mechanical,  the  Historical  and  the  Statistical." 
Science,  N.  S.,  1914. 


NATURE  OF  STATISTICAL  KNOWLEDGE     75 

are  in  their  essence  too  exact  for  precise  verifi- 
cation. They  are  verifiable  only  approximately. 
Hence,  since  they  demand  precise  verification,  we 
never  know  them  to  be  literally  true. 

"But  statistical  theories,  just  because  they  are 
deliberate  approximations,  are  often  as  verifiable 
as  their  own  logical  structure  permits.  They 
often  can  be  known  to  be  literally,  although 
only  approximately,  true." 

It  is  the  object  of  the  present  paper  to  discuss 
statistical  concepts  and  statistical  methods,  for 
the  purpose  of  trying  to  see  whether  these  methods 
do  in  fact  seem  to  lead  to  a  higher  kind  of  knowl- 
edge, and  are  hence  to  be  considered  destined  to 
become  the  exclusive  methods  of  science.  In 
this  discussion  let  us  endeavor  to  avoid  dogmatic 
assertion,  since,  in  the  first  place,  assertion  does 
not  really  get  us  far  in  the  search  for  truth,  and, 
in  the  second  place,  the  writer  himself  feels  in 
regard  to  this  question  very  far  from  that  serene 
consciousness  of  being  quite  unassailably  right 
which  is  essential  to  proper  dogmatism.  Indeed, 
it  is  for  the  purpose  of  definitely  formulating 
some  doubts,  which  have  grown  in  the  writer's 
mind  during  fifteen  years  in  which  the  greater 
part  of  his  time  and  energy  have  been  devoted  to 
the  application  of  statistical  methods  to  biological 
problems,  that  this  paper  is  written.  Very  likely 
some  will  not  agree  with  its  reasoning  or  its 
tentative  conclusions,  but  even  in  such  event,  it 


76    MODES  OF  RESEARCH  IN  ^GENETICS 

may  help  the  disagreeing  reader  to  the  more 
complete  classification  of  his  own  ideas  about 
statistical  concepts. 

II 

Let  us  first  consider  this  question  :  What  caused 
the  development  of  the  statistical  viewpoint  and 
method,  which  in  science  had  such  an  important 
growth  in  the  nineteenth  century?  For  what 
purposes  did  men  turn  to  the  statistical  method? 
This  question  has  been  very  ably  discussed  by 
Theodore  Merz  in  the  second  volume  of  his  "His- 
tory of  European  Thought  in  the  Nineteenth 
Century,"  and  we  cannot  do  better  than  follow 
his  development  of  the  matter.  Speaking  of  the 
origin  of  statistics,  Merz  says  {he.  cit.,  pp.  554- 
555) : 

"That  which  everywhere  oppresses  the  practical 
man  is  the  greater  number  of  things  and  events 
which  pass  ceaselessly  before  him,  and  the  flow 
of  which  he  cannot  arrest.  What  he  requires 
is  the  grasp  of  large  numbers.  The  successful 
scientific  explorer  has  always  been  the  man  who 
could  single  out  some  special  thing  for  minute  and 
detailed  investigation,  who  could  retire  with  one 
definite  object,  with  one  fixed  problem  into  his 
study  or  laboratory  and  there  fathom  and  un- 
ravel its  intricacies,  rising  by  induction  or  divi- 
nation to  some  rapid  generalization  which  allowed 
him  to  establish  what  is  termed  a  law  of  general 


NATURE  OF  STATISTICAL  KNOWLEDGE     77 

aspect  from  which  he  could  view  the  whole  or  a 
large  part  of  nature.  The  scientific  genius  can 
*stay  the  moment  fleeting';  he  can  say  to  the 
object  of  his  choice,  *Ah,  linger  still,  thou  art 
so  fair ' ;  he  can  fix  and  keep  the  star  in  the  focus 
of  his  telescope,  or  protect  the  delicate  fiber  and 
nerve  of  a  decaying  organism  from  succumbing  to 
the  rapid  disintegration  of  organic  change.  The 
practical  man  cannot  do  this ;  he  is  always  and 
everywhere  met  by  the  crowd  of  facts,  by  the 
relentlessly  hurrying  stream  of  events.  What 
he  requires  is  grasp  of  numbers,  leaving  to  the 
professional  man  the  knowledge  of  detail.  Thus 
has  arisen  the  science  of  large  numbers  or 
statistics,  and  the  many  methods  of  which  it  is 
possessed." 

Further  on  the  same  author  says  of  the  origin 
of  the  science  of  probability  {loc.  cit.,  pp.  567-568) : 

"The  necessity  of  having  recourse  to  elaborate 
countings,  to  registrations  of  births,  deaths,  and 
marriages,  to  lists  of  exports  and  imports,  to 
records  of  consumption  and  production  of  food- 
stuffs and  many  other  items,  forced  upon  those 
who  were  intrusted  with  the  gathering  and  using 
of  these  data  the  observation  that  all  such  knowl- 
edge is  incomplete  and  inaccurate.  Owing  to  the 
variability,  within  certain  limits,  of  recurring 
events  and  the  errors  of  counting  and  registration, 
we  have  to  content  ourselves  always  with  ap- 
proximation  instead   of   certainty.     Error   bulks 


78    MODES  OF  RESEARCH  IN  GENETICS 

very  largely  in  all  statistics,  and  vitiates  them; 
and  as  regards  coming  events,  our  minds  are  in  a 
state  of  expectation  rather  than  of  assurance. 
But  events  can  be  more  or  less  probable,  errors 
can  be  greater  or  smaller,  cumulative  or  compen- 
satory, and  our  expectations  may  be  well-  or  ill- 
founded.  And  so  there  has  arisen  the  science  of 
Probabilities  and  of  Chances,  and  the  Theory  of 
Error,  two  subjects  intimately  interwoven.  The 
former  arose  in  the  seventeenth  century  out  of 
the  frivolous  or  vicious  practice  of  betting  and 
gambling,  whilst  the  latter  was  founded  when 
astronomical  observations  accumulated,  and  the 
question  presented  itself  how  to  combine  them  so 
as  to  arrive  at  the  most  reliable  result." 

Now  from  these  two  quotations,  which  may 
certainly  be  considered  as  fairly  stating  the  case, 
it  is  apparent  that  those  circumstances  which  led 
men  to  turn  to  statistical  methods  of  reasoning 
and  investigation  were  not  such  as  grow  out  of 
an  increasing  precision  and  certainty  of  knowledge 
about  the  events  or  things  under  consideration, 
but  rather  were  quite  the  opposite.  In  other 
words,  the  statistical  point  of  view,  in  the  first 
instance,  was  adopted  as  an  admittedly  imper- 
fect means  of  getting  some  sort  of  knowledge 
about  a  class  of  events  concerning  which  it  was 
difficult  or  impossible  to  get  by  other  methods  the 
precise  or  particular  kind  of  knowledge  which 
was  wanted. 


NATURE  OF  STATISTICAL  KNOWLEDGE     79 

III 

A  careful  consideration  of  the  history  of  statis- 
tical science,  as  well  as  of  the  present  day  appli- 
cation of  these  methods,  leads  to  the  conclusion 
that  statistical  methods  are  used  for  two  sorts 
of  purposes,  or  to  gain  two  sorts  of  knowledge 
about  events  or  things. 

A.  On  the  one  hand  the  statistical  method 
finds  one  of  its  chief  uses  in  furnishing  a  method 
(and  the  only  one  known  in  science)  of  describing 
a  group  in  terms  of  the  group's  attributes,  rather 
than  in  terms  of  the  attributes  of  the  individuals 
which  compose  the  group.  This  important  use  of 
the  statistical  method  is  not  usually  formulated 
in  just  the  way  I  have  put  it  here,  or  in  an  earlier 
chapter  (p.  54).  On  that  account  it  may  be  well 
to  consider  the  point  a  little  more  analytically. 

What  sorts  of  positive,  definite,  and  exact 
knowledge  do  statistics  give  us? 

1.  Precise  knowledge  of  the  composition  of 
groups  or  masses.  This  is  the  knowledge  gained 
by  counting.  Suppose  we  find  a  basket  contain- 
ing a  number  of  balls  of  several  different  colors, 
and  proceed  to  count  them  with  the  following 
results : 

7   Reds 

9   White 

2   Black 

1    Green 


80    MODES  OF  RESEARCH  IN  GENETICS 

Such  a  count  furnishes  us  at  once  with  a  great 
deal  of  perfectly  definite  and  precise  information 
about  this  group  or  population  of  balls.  For 
example,  the  count  tells  us  that  it  will  never  be 
possible  to  draw  more  than  one  pair  of  balls  of 
which  one  member  is  green.  This  is  a  definite 
attribute  of  this  population  which  may  be  used  to 
differentiate  it  from  other  populations.  In  this 
particular  population  only  one  green  ball  occurs. 

This  sort  of  knowledge  derived  by  counting  is 
perfectly  definite  and  precise  so  far  as  relates  to  the 
particular  group  or  mass  which  it  concerns  in 
any  particular  case.  It  does  not  involve  any 
approximation,  or  probability,  and  is  as  precise 
as  knowledge  of  the  individual.  It,  however, 
pertains  to  the  group.  It  forms  a  part  of  a  proper 
scientific  description  of  a  group. 

2.  Knowledge  of  certain  abstract  qualities  of 
groups  or  masses.  This  knowledge  is  obtained  by 
calculation  from  the  counted  data.  The  more 
important  of  the  abstract  qualities  of  groups  are : 

a.  The  center  or  typical  condition  of  the  group ; 
or  the  condition  about  which  the  individuals 
composing  the  group  cluster.  This  is  variously 
measured :  by  the  arithmetic  mean,  which  gives 
the  center  of  gravity  of  the  group,  by  the  median, 
which  tells  the  point  on  either  side  of  which 
exactly  half  the  individuals  fall,  by  the  mode, 
which  tells  the  point  of  greatest  frequency  of 
occurrence  in  the  group,  etc. 


NATURE  OF  STATISTICAL  KNOWLEDGE     81 

b.  The  degree  of  individual  diversity  comprised 
in  the  group.  This  attribute,  called  the  varia- 
bility of  the  group,  is  again  variously  measured : 
by  standard  deviations,  coefficients  of  variation, 
etc. 

c.  The  degree  of  symmetry  of  the  distribution 
of  the  individuals  composing  the  group.  This  is 
measured  by  the  skewness  or  other  related  con- 
stants. 

d.  Various  other  attributes  of  distributions 
might  be  here  included,  such  as,  for  example,  the 
kurtosis,  but  for  purposes  of  the  present  general 
analysis  this  scarcely  seems  necessary.  Though 
some  of  these  attributes  involve  very  complex 
mathematical  expressions  for  their  measurement, 
the  general  fact  remains  clear  that  they  are  all 
attributes  of  groups  or  masses  which  are  described 
by  the  statistical  constants. 

One  point  here  we  must  be  quite  clear  about. 
This  is  that  the  kind  of  knowledge  discussed  under 
this  heading  2  is  just  as  definite  and  precise,  and 
involves  as  little  approximation  and  indetermin- 
ism,  as  does  any  piece  of  individualistic  knowledge, 
so  long  as  we  confine  our  attention  solely  to  the  par- 
ticular group  discussed  in  a  particular  single  case. 
We  are  accustomed  to  stating  means,  for  example, 
with  probable  errors.  But  this  is  only  because  it 
is  proposed  to  extend  the  conclusions  beyond  or 
outside  of  the  particular  group  and  the  particular 
instance  for  which  the  mean  was  calculated.     For 


82    MODES  OF  RESEARCH  IN  GENETICS 

that  group  and  that  instance  the  mean  is  perfectly 
exact  and  precise  to  that  degree  of  precision  de- 
noted by  the  unit  of  measure  used,  assuming  that 
no  arithmetical  mistakes  have  been  made  in  its 
computation.  Thus  suppose  one  measures  the 
stature  of  three  men  to  the  nearest  inch,  and  then 
calculates  the  average.  The  result  is,  without  any 
probable  error,  the  average  height,  at  the  particu- 
lar moment  when  they  were  measured,  of  those 
three  men  exact  to  the  unit  of  measurement  used. 
It  describes  and  measures  precisely  an  attribute 
of  those  men  considered  as  a  group.  But  if  we 
were  to  consider  this  result  from  the  viewpoint 
of  whether  it  gave  a  reasonable  measure  of  the 
average  height  of  men  in  general,  or  from  the 
viewpoint  of  whether  it  gave  a  proper  value  for 
the  mean  height  of  these  men  when  repeatedly 
measured  under  varying  conditions,  it  would  clearly 
be  subject  to  a  large  probable  error.  It  would, 
in  point  of  fact,  have  lost  its  character  of  precise 
and  definite  knowledge,  and  have  become  a  more 
or  less  poor  approximation. 

3.  Precise  knowledge  of  the  degree  of  association 
or  contingency  between  different  events  or  char- 
acters within  a  group.  This  is  furnished  by  the 
method  of  correlation  in  one  or  another  of  its  vari- 
ous forms.  By  this  general  method  we  are  able  to 
measure  precisely  the  degree  of  resemblance  be- 
tween the  individuals  composing  a  group  in  respect 
to  one  or  more  characters.     So  long  as  attention 


NATURE  OF  STATISTICAL  KNOWLEDGE     83 

is  confined  to  the  particular  group  on  which  the 
measurement  is  made,  and  to  that  group  alone, 
and  to  a  single  instance  (in  time)  the  knowledge 
gained  is  precise.  It  is  a  part  of  the  description 
of  the  attributes  of  that  group.  When  we  pass 
from  that  particular  group  to  other  groups  or 
individuals  our  results  are  no  longer  precise,  but 
inferential,  and  the  probable  errors  tell  us  some- 
thing about  the  degree  to  which  the  inference  is 
trustworthy. 

Summarizing  the  results  of  the  above  analysis, 
we  see  that  the  statistical  method  can 

1.  Furnish  precise  descriptive  knowledge  about 
groups.  This  knowledge  is  of  various  sorts.  It 
is  definite  and  precise  so  long  as  attention  is  con- 
fined solely  to  the  particular  group  and  the  par- 
ticular instance  on  which  it  is  based. 

2.  The  knowledge  gained  by  the  statistical 
method,  as  we  have  analyzed  it  above,  precise 
though  it  may  be,  pertains  to  the  group  and  not  to 
the  individual.  It  is  exact  knowledge  about  the 
composition,  or  attributes,  or  contingencies  of 
masses  or  groups. 

3.  This  ability  to  describe  groups  in  terms  of 
the  groups'  own  attributes,  which  is  an  unique 
property  of  the  statistical  method,  is  extremely 
useful  in  the  practical  conduct  of  scientific  in- 
vestigations. It  makes  the  statistical  method  an 
absolutely  essential  adjunct  to  every  other  scien- 
tific method,  and  particularly  to  the  experimental. 


84    MODES  OF  RESEARCH  IN  GENETICS 

This  fact  is  just  now  beginning  to  be  recognized 
by  some  experimentalists  and  hailed  as  a  rather 
original  thought.     It  is  not  new. 

B,  We  may  turn  now  to  a  wholly  different 
aspect  of  the  statistical  method,  wherein  it  is 
used  for  the  purpose  of  predicting  or  estimating 
the  probable  or  the  approximate  condition  in  the 
individual  from  a  statistical  examination  of  the 
condition  in  the  mass  or  the  group.  Resort  is 
had  to  the  statistical  method  for  this  purpose 
primarily  in  those  cases  where  the  outcome  of 
the  event,  or  the  condition  of  the  thing,  is  deter- 
mined by  the  combined  action  of  a  large  number  of 
small  causes,  each  about  equally  influential  upon 
the  final  result. 

Originally  the  statistical  method  was  only 
employed  for  this  second  purpose  in  cases  where, 
because  of  the  multiplicity  of  the  cause  groups 
involved  in  the  determination  of  the  event,  and 
the  consequently  small  effect  of  each,  it  was 
impossible  to  make  any  reasonable  prediction  re- 
garding an  individual  from  an  examination  of  that 
individual  alone.  Such  employment  might  be 
considered  legitimate,  though  not  very  fruitful, 
on  the  ground  that  prediction  so  made,  uncertain 
and  doubtful  as  it  may  be,  is  after  all  perhaps 
better  than  no  prediction  at  all.  As  time  has  gone 
on,  however,  there  has  been  an  increasing  tendency 
to  assume  that  this  use  of  the  statistical  method 
had  general  a  priori  validity  and  could  be  profitably 


NATURE  OF  STATISTICAL  KNOWLEDGE     85 

employed  in  all  sorts  of  cases.  This  point  of 
view  reaches,  it  seems  to  me,  its  limit  in  the  sen- 
tence already  quoted  from  Royce,  which  I  venture 
to  repeat  with  one  word  italicized.  "There  is, 
therefore,  good  reason  to  say  that  not  the  mechan- 
ical but  the  statistical  form  is  the  canonical 
form  of  scientific  theory,  and  that  if  we  knew  the 
natural  world  millions  of  times  more  widely  and 
minutely  than  we  do,  the  mortality  tables  and  the 
computations  based  upon  a  knowledge  of  aver- 
ages, would  express  our  scientific  knowledge  about 
individual  events,  much  better  than  the  nautical 
almanac  would  do." 

This  leads  us  to  consider  carefully  the  general 
question  of  the  validity  on  the  one  hand,  and  the 
usefulness  on  the  other  hand,  of  this  whole  second 
mode  of  employment  of  the  statistical  method. 
It  is  the  one  which  has  attracted  the  greatest 
attention  because  of  its  essentially  spectacular 
nature  coupled  with  a  sort  of  mysteriousness 
bordering  upon  the  miraculous.  It  seems  a 
wonderful,  indeed  almost  a  superhuman,  accom- 
plishment to  be  able  to  say  in  the  manner  of  the 
oracles  of  old,  "So  many  men  will  commit  suicide 
next  year." 

IV 

Since  Clerk-Maxwell  introduced  statistical 
modes  of  reasoning  into  physical  science  there  has 
been  an  ever  increasing  tendency  to  regard  the 


86    MODES  OF  RESEARCH  IN  GENETICS 

universe  as  organized  on  a  statistical  plan.  This 
has  come  to  carry  with  it  two  implications,  one 
of  which  is  quite  fallacious  and  the  other  partly 
so. 

The  first  of  these  is  that  the  individual  events, 
of  which  all  the  causes  are  not  precisely  known  to 
us,  are  indeterminate.  Such  an  assumption  is  of 
course  unwarranted.  Because  we  do  not  know  all 
the  causes  leading  to  a  particular  event  does  not 
mean  that  that  event  is  any  the  less  precisely 
determined  by  the  course  of  antecedent  events. 
Consider  a  box  containing  100  consecutively 
numbered  cards.  Suppose  one  card  were  to  be 
drawn  and  that  it  bore  the  number  36.  It  would 
be  quite  impossible  to  formulate  precisely  all  the 
causes  which  led  to  the  drawing  of  the  number 
36  on  the  particular  occasion  considered,  but  it 
is  equally  impossible  to  conceive  that  this  result 
was  not  definitely  "caused."  In  other  words, 
there  clearly  was  a  whole  train  of  antecedent 
circumstances,  which  taken  all  together  definitely 
resulted,  and  could  only  have  residted,  in  the  draw- 
ing of  the  number  36.  The  too  prevalent  con- 
clusion that  the  application  of  the  statistical 
method  or  statistical  modes  of  thought  implies 
phenomenal  indeterminism  in  the  individual  case 
is  totally  fallacious. 

The  second  currently  accepted  implication  of  a 
statistical  view  of  the  universe  is  that  in  general 
a  particular  event  or  phenomenon  is  the  outcome 


NATURE  OF  STATISTICAL  KNOWLEDGE     87 

of  the  combined  action  of  a  great  number  of 
causes,  each  of  which  alone  produced  but  a  small 
part  of  the  final  total  effect.  There  is  clearly  so 
much  truth  in  this  point  of  view  as  is  included  in 
the  fact  that  individual  events  or  phenomena  do, 
in  some  degree  or  other,  vary,  and  further  these 
variations  in  general  distribute  themselves  more 
or  less  in  accord  with  the  well-known  laws  of  errors. 
But  the  assertion  that  events  are  individually 
the  outcome  of  the  action  of  great  numbers  of 
causes,  each  of  which  had  a  small  part  and  a 
part  significantly  equal  to  that  played  by  every 
other  one  of  the  causes  concerned  in  the  final 
result,  is  only  true  if  the  "universe  of  discourse" 
is  indefinitely  extended  in  time.  But  ^practically 
science  works  in  a  definitely  and  rather  narrowly 
limited  universe  of  discourse  so  far  as  concerns 
time.  One  of  the  causes  for  the  writing  of  these 
lines  is  that  a  certain  worthy  was  not  shipwrecked 
in  voyaging  to  this  country  nearly  300  years  ago, 
since  if  he  had  been  shipwrecked  presumably  I 
should  not  exist  and  therefore  could  not  write 
these  words.  But  practically  this  cause  had  very 
little  to  do  with  determining  that  I,  being  here  in 
existence,  should  write  this  book  rather  than  do 
various  other  things  which  I  might  have  done 
instead.  It  undoubtedly  is  true  that  a  vast 
number  of  small  causes  do  play  a  part  in  the 
determination  of  any  particular  event.  But,  in 
many  of  the  events,  at  least,  in  which  science  is 


88    MODES  OF  RESEARCH  IN  GENETICS 

interested,  these  multitudinous  minor  causes  do  not 
play  any  significant  part  in  the  differential  deter- 
mination of  a  particular  event  at  a  particular  in- 
stant of  time.  There  is  in  connection  with  the 
causation  of  most  events  some  one  or  two,  or  at 
most  a  very  few,  outstanding  cause  groups  which, 
for  all  practical  purposes,  at  a  given  moment  com- 
pletely determine  their  occurrence.  The  total 
effect  of  all  the  vast  number  of  other  minor  causes 
concerned  in  the  remote  past  is  so  minute,  as  com- 
pared with  the  part  played  by  the  really  determina- 
tive ones  at  the  moment,  as  to  be  negligible.  In 
other  words,  all  natural  cause  groups  are  not  small, 
nor  of  equal  (balanced)  values  in  the  final  deter- 
mination of  the  event  to  which  they  relate,  pro- 
vided we  confine  ourselves  to  the  time  limits  of 
finite  practical  operations.  Yet  something  very 
much  of  that  sort  seems  to  me  to  be  implicitly 
involved  in  any  such  generalized  statistical  view 
of  the  universe  as  that  which  Professor  Royce 
holds  up  for  our  admiration  as  a  sort  of  scientific 
ideal. 

The  fact  that  all  natural  causes  or  cause  groups 
are  not  equally  significant  quantitatively  is,  of 
course,  what  makes  the  experimental  method 
fruitful  —  one  might  even  say  possible  —  in  sci- 
ence. The  very  essence  of  the  experimental 
method  is  that  the  conditions  for  the  happening 
of  an  event  are  so  arranged  that  the  influence  of 
one  putative  causal  factor  may  be  tested  at  a 


NATURE  OF  STATISTICAL  KNOWLEDGE     89 

time.  If  with  a  radical  change  in  this  one  factor, 
whilst  all  others  remain,  so  far  as  may  be,  con- 
stant, no  change  in  the  happening  of  the  event  is 
observed,  the  experiment  has  shown  that  this 
particular  factor  has  no  significant  causal  relation 
to  the  happening  of  the  event.  If  a  marked 
change  in  the  happening  of  the  event  is  observed 
always  to  follow  the  change  of  conditions  of 
operation  of  the  factor  under  investigation,  then 
clearly  this  factor  plays  a  determinative  part.^ 
In  other  words,  it  is  a  fundamental  logical  pre- 
requisite of  the  experimental  method  if  it  is  to 
be  successful  (that  is,  contribute  to  knowledge) 
that  it  operate  in  a  universe  in  which  all  causal 
factors  are  not  of  equal  quantitative  significance 
at  any  given  instant  of  time. 

Clearly  experimental  analysis  of  this  sort 
would  have  quickly  discovered,  if  the  common 
sense  of  men  had  not  long  previously  shown,  that 
the  course  which  a  particular  event  is  going  to 
take  is  not  immediately  the  result  of  the  action  of 
an  indefinitely  large  number  of  individually  in- 
significant causal  factors,  but  that  it  is  the  out- 
come of  the  action  of  a  few  immediately  deter- 
minative factors  and  the  effect  of  the  indefinitely 
large  number  of  historically  antecedent  small 
causes  is  insignificant  in  the  sense  of  being  differ- 
ential.    Generalized,   the   point   may   be   put   in 

1  Cf.  Jennings'  valuable  paper  on  radical  experimental  analysis 
already  referred  to  in  an  earlier  chapter  (p.  13,  supra). 


90    MODES  OF  RESEARCH  IN  GENETICS 

this  way :  an  event  A  is  about  to  happen.  It 
may  happen  in  any  one  of  n  different  ways,  each 
one  of  which  ways  may  be  designated  by  a  letter, 
Z,  p,  r,  t,  etc.  Now  an  indefinitely  large  number  of 
causes  are  concerned  in  bringing  it  about  that 
the  event  A  is  going  to  happen,  and  that  it  can 
equally  well  happen  either  as  /,  p,  r,  t,  etc.  In 
other  words,  the  setting  of  the  stage  for  the  event 
has  involved  a  vast  number  of  small  and  balanced 
causes.  But  the  causes  which  are  differential  in 
the  particular  case,  that  is,  which  determine  that 
A  shall  happen  in  the  p  way  this  particular  time, 
and  not  in  the  /,  the  t,  or  any  other  way,  are,  in 
general : 

1.  Few  in  number. 

2.  Immediate  in  time. 

3.  Large  in  relative  quantitative  effect. 

The  point  under  discussion  may  perhaps  be 
made  plainer  by  a  homely  illustration.  Suppose 
a  man  steps  up  behind  a  mule  and  prods  the 
creature  with  his  walking  stick.  The  human  in- 
tellect is  unequal  to  the  task  of  predicting  exactly, 
in  the  particular  case,  what  precise  portion  of  the 
man's  body  the  mule's  hoof  will  land  upon.  A 
multitude  of  minor  causes  will  affect  this  :  the 
relative  height  of  the  man  and  the  mule,  the  age 
of  each,  the  place  poked  with  the  walking  stick, 
the  degree  of  fatigue  of  the  mule,  the  temperature, 
the  season  of  the  year,  and  countless  other  things 


NATURE  OF  STATISTICAL  KNOWLEDGE     91 

have  an  influence  in  determining  just  the  precise 
spot  where  the  mule's  foot  and  the  man's  body 
come  together.  These  could  be  investigated 
statistically  and  tables  drawn  up  from  which  one 
could  predict  the  part  of  the  man  which  would 
most  probably  receive  the  hoof.  But  what  a 
silly,  futile  piece  of  business  this  all  would  be,  since 
clearly  the  influence  of  all  of  these  small  causes 
on  what  happens  to  the  man  is  stupendously  over- 
shadowed by  the  results  of  two  factors;  namely, 
putting  himself  behind  a  mule  and  prodding  the 
animal  with  a  stick.  Of  course,  a  vast  number  of 
antecedent  causes  are  involved  in  the  setting  of 
the  stage,  but  these  are  not  differential  in  the 
determination  of  the  end  event  of  the  series. 

The  preceding  illustration  has  nothing  directly 
to  do  with  science,  but  the  essential  point  involved 
operates  in  the  use  of  the  statistical  method  as  a 
weapon  of  scientific  research.  This  method  being, 
as  we  have  seen  elsewhere,  only  a  descriptive 
method,  it  cannot,  any  more  than  any  other 
descriptive  method,  tell  us  anything  directly  about 
the  causes  involved  in  the  determination  of  any 
events  or  phenomena  under  consideration.  It 
may  be  of  great  aid,  in  combination  with  the 
experimental  method,  in  helping  to  arrive  at  such 
knowledge,  but  alone  and  of  itself  it  cannot 
directly  furnish  knowledge  of  causes  of  individual 
events.  Yet  the  statistical  method,  particularly 
in  that  phase  of  it  which  we  have  here  under  dis- 


92    MODES  OF  RESEARCH  IN   GENETICS 

cussion,  which  essays  to  predict  the  probable 
condition  of  the  individual  from  the  knowledge 
of  the  mass,  seems  to  furnish  information  about 
causes.  It  wears  a  specious  air  of  bringing  a 
kind  of  knowledge  which  in  reality  it  not  only 
never  does,  but  from  the  very  nature  of  the  case 
never  can  furnish. 

V 

Let  us  consider  now  a  little  more  in  detail  the 
nature  of  the  prediction  of  the  probable  condition 
of  the  individual  from  a  knowledge  of  the  mass  or 
group.  It  has  been  shown  in  an  earlier  section 
(p.  83)  that  statistics  give  perfectly  definite  and 
precise,  and  often  very  useful  knowledge  about 
masses  or  groups.  We  are  now,  however,  not 
concerned  with  this  as  group  knowledge,  but 
rather  with  one  use  to  which  such  knowledge  has 
been  put.  This  use  is  that  which  is  comprised 
in  the  subject  of  statistical  probabilities,  and 
which  involves  the  drawing  of  conclusions  as  to 
the  probable  condition  of  the  individual,  based  on 
an  exact  knowledge  of  the  mass. 

In  order  to  approach  the  subject  in  the  simplest 
way  let  us  consider  a  concrete  case.  Suppose  a 
problem  of  the  following  sort  were  to  be  set  before 
us  for  answer :  What  is  the  probability  that, 
at  some  chosen  moment  of  time,  the  next  birth  to 
occur  in,  let  us  say,  the  city  of  Baltimore,  will  be 
of  a  white  child.     Now  if  we  look  at  this  as  a 


NATURE  OF  STATISTICAL  KNOWLEDGE     93 

question  in  statistical  probability  the  appropriate 
way,  of  course,  to  go  about  solving  it  is  to  turn  up 
the  registration  reports  for  the  city  of  Baltimore 
covering  a  period  of  years,  and  find  out  what  is  the 
proportion  of  white  to  colored  births  in  that  city. 
Then,  by  the  simplest  theorem  in  the  calculus  of 
chance,  the  probability  that  the  next  birth  will  be 
of  a  white  child  will  be  given  by  a  fraction  of 
which  the  numerator  is  the  number  of  white 
children  born  in  Baltimore  and  the  denominator 
is  the  total  number  of  children  born  in  Baltimore, 
both  figures  including  the  same  period  of  time. 
The  difference  between  the  fraction  so  obtained 
and  1  will  be  the  probability  that  the  next  birth 
will  be  of  a  child  not  white ;  that  is,  colored.  When 
we  have  obtained  such  a  fraction  we  have  a  definite 
piece  of  statistical  knowledge,  but  of  just  what  use 
is  it  so  far  as  concerns  the  individual  case.^  It 
implies  no  biological  knowledge  of  any  kind ; 
no  knowledge  of  the  laws  of  heredity.  It  really 
adds  essentially,  it  seems  to  me,  to  the  sum  total 
of  the  world's  knowledge  only  one  thing.  That 
thing  is  the  proper  betting  odds  on  what  the 
color  of  the  next  child  born  in  the  city  will  be. 
This  knowledge  would  really  be  useful,  in  a 
pragmatic  sense,  only  provided  some  one  wishes 
to  gamble  upon  that  event. 

Of  course  the  statistical  count,  on  which  the 
probability  is  based,  in  itself  furnishes  definite 
and  precise  information  about  the  population  of 


94    MODES  OF  RESEARCH  IN  GENETICS 

Baltimore,  as  a  ^population.  This  may  be  useful. 
What  we  are  now  considering,  though,  is  knowl- 
edge about  individual  cases. 

Let  us  see  what  a  totally  different  kind  of 
ability  to  predict  the  future  event  in  an  individual 
case  is  gained  when  we  take  into  account  one 
single  biological  fact  of  an  individualistic  instead 
of  a  statistical  character.  Suppose,  that  is  to 
say,  that  we  are  informed  that  the  mother  of  the 
next  baby  to  be  born  in  Baltimore  is  black.  It 
needs  no  argument  to  show  how  much  more 
precise  is  our  prediction  as  to  the  color  of  the 
next  baby  under  these  conditions. 

This  illustration  brings  out  clearly  the  difference 
between  the  two  possible  bases  for  the  prediction 
of  a  future  event.  On  the  one  hand,  such  pre- 
diction may  be  based  on  statistical  ratios.  This 
means  merely  a  count  of  an  indefinitely  large  past 
experience  regarding  the  occurrence  or  failure  of 
the  event,  but  in  no  way  takes  into  account  the 
causes  which  underlie  the  happening  of  the  event 
in  any  particular  case.  On  the  other  hand,  we 
have  the  prediction  which  is  based  on  a  definite 
knowledge  of  the  determinative  causes  which  bring 
about  the  happening  of  a  particular  individual 
event  of  the  sort  in  which  we  are  interested  and 
about  which  we  are  to  predict.  There  can  be,  it 
would  seem,  no  comparison  between  the  usefulness, 
in  the  pragmatic  sense,  of  these  two  kinds  of 
knowledge.     The  statistical  knowledge  on  which 


NATURE  OF  STATISTICAL  KNOWLEDGE  .  95 

a  statistical  prediction  is  made  is  essentially  the 
most  sterile  kind  of  knowledge  that  one  can 
possibly  have  so  far  as  concerns  the  individual 
event.  It  merely  gives  one  the  betting  odds  for 
or  against  the  occurrence  of  an  event,  and  abso- 
lutely nothing  more.  Now  a  wager,  however 
large,  in  the  scientific  sense  neither  discovers, 
expounds,  nor  is  a  criterion  of  the  truth.  Bets, 
in  other  word,  are  not  evidence,  though  the 
statistician  sometimes  seems  to  forget  this,  and 
to  deal  with  statistical  ratios  as  though  they  had 
probative  worth  in  regard  to  phenomena. 

On  the  other  hand,  a  prediction  based  on  ex- 
perimentally acquired  knowledge  of  the  deter- 
minative cause  of  the  individual  event  brings  with 
it  a  real  knowledge  of  a  natural  phenomenon. 
The  predictions  so  made  may  not  always  turn 
out  correct,  but  when  they  do  not,  it  incites  us  to 
investigate  the  particular  disturbing  factor  which 
under  such  circumstances  may  overwhelm  the 
normally  determinative  cause  of  a  particular 
event. 

VI 

Man  soil  das  Kind  nicht  mit  dem  Bade  verschiitten. 
The  critical  reader  may  be  inclined  to  think  that 
this  is  exactly  what  the  discussion  in  the  preced- 
ing sections  has  done.  If,  as  has  there  been  sug- 
gested, that  part  of  the  statistical  method  which 
uses  the  calculus  of  probability  as  a  basis  for  the 


96    MODES  OF  RESEARCH  IN  GENETICS 

prediction  of  future  events,  gives  only  a  knowl- 
edge of  betting  odds,  one  may  ask :  what  about 
the  whole  concept  of  probable  error?  The  value 
of  this  concept  in  scientific  research  is  unquestioned 
(cf.  p.  59,  supra).  Yet  plainly  the  whole  concept 
has  its  basis  in  the  calculus  of  probability.  Has 
not  our  discussion  led  us  unwittingly  into  a  serious 
contradiction  ? 

I  think  not.  Let  us  examine  the  probable  error 
concept  a  little  more  carefully  than  we  have  yet 
done.  Suppose  we  read  that  the  mean  length  of 
the  thorax  of  a  thousand  fiddler  crabs  is  30.14  ±  .02 
mm.  Just  what  does  this  actually  mean  ?  Ac- 
cepting the  figures  at  their  face  value,  or,  put 
another  way,  assuming  that  the  mathematical 
theory  on  which  the  probable  error  was  calculated 
was  the  correct  one,  the  figures  mean  something 
like  this :  If  one  were  to  take,  quite  at  random, 
successive  samples  of  1000  each  from  the  total 
population  of  fiddler  crabs  and  determine  the  mean 
thoracic  length  from  each  sample,  these  means 
would  all  be  different  from  each  other  by  varying 
amounts.  In  other  words,  no  single  sample 
would  give  us  the  absolutely  true  value  of  the 
mean  thoracic  length  of  the  whole  fiddler  crab 
'population.  This  true  value  is  in  an  absolute 
sense  unknowable,  because,  for  one  reason,  always 
we  must  come  at  the  finding  of  it  by  the  way  of 
random  sampling,  and  sampling  means  variation. 
Now  it  is  an  observed  fact  of  experience  that  the 


NATURE  OF  STATISTICAL  KNOWLEDGE     97 

variations  due  to  random  sampling  distribute 
themselves  according  to  a  definite  law  of  mathe- 
matical probability.  Knowing  this  law,  it  is 
clearly  possible  to  state  the  mathematical  proba- 
bility for  (or  against)  any  particular  deviation  or 
variation  occurring  as  the  result  of  random  sam- 
pling. Exactly  this  is  what  the  probable  error  does. 
It  says,  in  the  particular  case  here  considered, 
that  it  is  an  even  chance,  that  a  deviation  or 
variation  in  the  value  of  the  mean  as  great  as  or 
greater  than  .02  mm.  above  or  below  will  occur 
as  a  result  of  random  sampling.  Or,  put  in 
another  way,  if  we  took  successive  samples  of 
1000  each  from  this  crab  population,  it  is  an  even 
bet  that  the  value  of  the  mean  from  any  sample 
would  fall  between  30.14  +  .02  =  30.16,  and 
30.14  -  .02  =  30.12. 

Now  all  the  knowledge  that  this  probable 
error  furnishes  is  this  :  that  if  a  man  were  to  say, 
"I'll  bet  a  thousand  dollars  that  the  mean  thoracic 
length  of  the  next  sample  of  fiddler  crabs  you 
measure  will  be  either  over  30.16  mm.  or  under 
30.12  mm.,"  one  would  not  be  justified  in  offering 
odds.  He  could  wager  on  even  terms.  Either 
party  involved  in  the  transaction  would  be  as 
likely  to  lose  (or  to  win)  as  the  other. 

Putting  the  case  in  this  way,  it  is  clear  that  this 
is  the  same  kind  of  knowledge  which  comes  from 
an  examination  of  probable  errors  as  that  dis- 
cussed in  the  preceding  section.     It  is  a  knowledge 


98    MODES  OF  RESEARCH  IN  GENETICS 

of  betting  odds.  It  has  no  necessary  relation 
per  se  to  any  physical,  chemical,  or  biological  laws. 
It  merely  informs  one  how  he  may  safely  gamble 
on  an  event  if  he  is  so  minded  and  can  find  some 
one  else  ready  to  do  the  same  thing. 

Wherein  lies  the  value  of  the  probable  error 
concept  for  science,  then.^  Simply  in  that  it 
serves  as  a  test  or  check  on  every  mode  of  research 
in  science.  So  far  as  I  can  see,  the  calculus  of 
probability,  in  and  of  itself  alone,  is  not  and 
never  can  be  an  effective  weapon  of  research  for 
the  discovery  of  truth  in  phenomenal  science,  be 
it  physical  or  biological.  Yet  it  operates  as  an 
ever-present  test  of  the  trustworthiness  of  the 
results  obtained  by  modes  of  research  which  are  in 
themselves  adapted  to  making  discoveries  about 
phenomena.  The  student  of  probability  says 
something  like  this  to  the  experimentalist :  "Yours 
is  the  way  to  find  out  the  significant  underlying 
causes  of  phenomena.  Let  it  be  practiced  with 
all  zeal,  but  let  it  be  remembered  that  you  operate 
in  a  finite  way  in  a  finite  universe,  and  conse- 
quently all  your  results  are  subject  to  such  fluc- 
tuations and  variations  as  experience  has  shown 
arise  from  random  sampling.  I  regret  that  I 
cannot  directly  and  alone  discover  significant 
causes,  but  at  any  rate  I  can  furnish  you  a  test 
whereby  you  may  reasonably  judge  whether  your 
result  is  significantly  influenced  by  these  fluctu- 
ations of  random  sampling." 


NATURE  OF  STATISTICAL  KNOWLEDGE     99 

VII 

To  sum  the  whole  matter  up :  I  have  tried  to 
show  that  the  statistical  method  in  science  has 
been  used  to  do  two  things. 

The  first  of  these  is  a  unique  function  of  the 
method  —  to  furnish  a  description  of  a  group  of 
objects  or  events  in  terms  of  the  group's  attributes 
rather  than  those  of  the  individuals  composing 
the  group.  Herein  lies  the  great  value  of  the 
statistical  method.  It  is,  however,  a  descriptive 
method  only  and  has  the  limitations  as  a  weapon 
of  research  which  that  fact  implies. 

The  second  purpose  that  the  statistical  method 
has  been  called  upon  to  accomplish  is  the  predic- 
tion of  the  individual  case  from  a  precise  knowl- 
edge of  the  group  or  mass.  This  involves  some- 
thing really  additional  to  the  statistical  method  per 
se;  namely,  the  mathematical  theory  of  probabil- 
ity. We  have  seen  that  this  side  of  the  statistical 
method  gives  only  a  somewhat  sterile  kind  of 
knowledge  so  far  as  concerns  individuals ;  namely, 
a  knowledge  of  betting  odds.  The  theory  of  prob- 
ability grew  up  about  the  gaming  table,  not  in  the 
laboratory.  Its  place  in  the  methodology  of  sci- 
ence is  not  an  independent  one.  By  it  alone  one 
cannot  discover  new  truths  about  phenomena. 
But  it  is  a  highly  important  adjunct  to  other 
modes  of  research. 

Plainly,  however,  one  cannot  regard  statistical 


100    MODES  OF  RESEARCH  IN  GENETICS 

knowledge  in  general  as  a  higher  kind  of  knowledge 
than  that  derived  in  other  ways.  Nor  is  the 
statistical  method  to  become  the  dominant  or 
exclusive  method  of  science,  though  it  will  always 
be  useful,  and  in  many  fields  an  essential  method. 
It  will  find  its  chief  usefulness,  first  in  its  sphere 
of  furnishing  shorthand  descriptions  of  groups, 
and  second  in  furnishing  a  test  of  the  probable 
reliability  of  conclusions. 


CHAPTER  IV 

CERTAIN    LOGICAL    AND    MATHEMATICAL     AS- 
PECTS OF  THE  PROBLEM  OF    INBREEDING  ^ 

I.   The   Analysis   and    Measurement   of   In- 
breeding 

The  effect  of  inbreeding  on  the  progeny  is  a 
much-discussed  problem  of  theoretical  biology 
and  of  practical  breeding.  It  has  been  alternately 
maintained,  on  the  one  hand,  that  inbreeding  is 
the  most  pernicious  and  destructive  procedure 
which  could  be  followed  by  the  breeder,  and  on  the 
other  hand,  that  without  its  powerful  aid  most  of 
what  the  breeder  has  accomplished  in  the  past 
could  not  have  been  gained  and  that  it  offers  the 
chief  hope  for  further  advancement  in  the  future. 
While  there  is  now,  among  animal  breeders  at 
least,  a  more  widespread  tendency  than  was 
formerly  the  case  towards  the  opinion  that  in- 
breeding jper  se  is  not  a  surely  harmful  thing, 
nevertheless  this  opinion  is  by  no  means  univer- 
sally held,  and  in  any  case  does  not  rest  upon  a 
definite    and    well-organized    body    of    evidence. 

1  This  paper  is  based  upon  a  series  of  "Studies  on  Inbreeding" 
which  have  recently  been  published,  chiefly  in  the  American  Naturalist, 
during  1913,  1914,  and  1915. 

101 


102    MODES  OF  RESEARCH  IN  GENETICS 

Aside  from  a  relatively  small  amount  of  definite 
experimental  data  one's  judgment  is  finally  formed 
on  the  basis  of  his  interpretation  of  the  vast 
accumulation  of  material  comprised  in  the  recorded 
and  unrecorded  experience  of  the  breeders  of 
registered  (pedigreed)  livestock. 

This  material  recorded  in  the  books  of  registra- 
tion far  exceeds  in  amount  and  in  diversity  any 
which  could  possibly  be  obtained  experimentally 
on  the  same  forms  of  life.  It  must  be  said,  how- 
ever, that  the  discussion  of  it  with  a  view  to  an 
analysis  of  the  effects  of  inbreeding,  though  under- 
taken at  greater  or  less  length  by  a  number  of 
men  including  Lehndorff,  von  Oettingen,  Bruce 
Low,  Hoesch,  Chapeaurouge,  Bunsow,  Strang, 
and  others,  has  not  led  to  results  characterized 
by  the  precision,  the  definiteness,  or  the  quality  of 
getting  at  fundamentals  demanded  in  the  present 
state  of  the  science  of  genetics. 

The  lack  of  precision  and  fundamental  character 
in  the  studies  alluded  to  is  not  primarily  to  be 
attributed  to  any  inherent  defect  in  the  material. 
In  the  breeding  of  all  of  the  domestic  animals 
inbreeding  has  been  practiced ;  in  many  instances 
to  a  very  marked  degree.  Further,  the  manner  in 
which  the  inbreeding  has  been  done  (the  types  of 
relationship-matings)  exhibits  a  most  intricate 
diversity,  from  which  different  types  may  be 
picked  out  for  analysis  in  any  reasonable  quantity. 
The  records  are  accurate,  within  their  limitations. 


\ 


THE   PROBLEM  OF  INBREEDING       103 

to  a  high  degree.  Probably  no  experimentaHst's 
records  of  descent  are  more  accurate,  considering 
the  relative  numbers  involved  in  the  two  cases. 

The  real  need,  I  venture  to  think,  has  been  for 
an  appropriate  and  valid  method  of  pedigree 
analysis,  which  possessed  generality,  and  could  on 
that  account  be  depended  on  to  give  comparable 
results  when  applied  to  two  (or  more)  different 
pedigrees.  Specifically,  there  seems  not  to  have 
been  worked  out  any  adequate  general  method  of 
measuring  quantitatively  the  degree  of  inbreeding 
which  is  exhibited  in  a  particular  pedigree.  Without 
such  a  measure  it  is  clearly  impossible  to  proceed  far 
in  the  analysis  of  the  kinship  aspect  of  inbreeding. 

It  is  the  purpose  of  this  paper  to  present  a 
method  for  measuring  and  expressing  numerically, 
in  the  form  of  coefficients,  the  degree  of  inbreeding 
which  exists  in  any  particular  case.  I  shall 
endeavor  to  show  that  the  method  is  (a)  unique, 
in  the  sense  that  the  values  obtained  in  any  par- 
ticular instance  can  only  be  affected  by  the  degree 
or  amount  of  inbreeding  which  has  been  practiced 
in  the  line  of  descent  under  consideration,  and 
(b)  general,  in  the  sense  that  it  is  equally  applicable 
to  all  pedigrees  and  to  all  degrees  and  types  of  in- 
breeding. 

Preliminary  Definitions 

In  attempting  any  general  analysis  of  the  prob- 
lem  of    inbreeding    from  the    theoretical   stand- 


104    MODES  OF  RESEARCH  IN  GENETICS 

point  one  is  confronted  with  the  necessity  for  a 
definition  of  inbreeding  which  shall  be  at  once 
precise  and  general,  that  is,  such  as  to  include  all 
of  the  many  diverse  ways  in  which  this  sort  of 
breeding  may  be  practiced.  A  great  number  of 
definitions  of  the  concept  "inbreeding"  have  been 
proposed  in  the  literature  of  genetics.  I  shall  not 
attempt  to  review  these  definitions  here,  since  to 
do  so  would  serve  no  useful  purpose  in  the  present 
connection.  A  careful  consideration  of  them  is 
bound,  I  think,  to  lead  one  to  the  conclusion  that 
they  have  been,  in  general,  based  on  grounds  of 
practical  expediency  rather  than  critical  biological 
analysis. 

Clearness  and  simplicity  of  thinking  will  be 
gained  by  approaching  the  problem  de  novo. 
Leaving  aside  for  the  moment  all  consideration  of 
details  as  to  how  a  particular  piece  of  inbreeding 
is  done,  it  is  clear  that  underlying  all  definitions  of 
inbreeding  is  to  be  found  the  concept  of  a  narrowing 
of  the  network  of  descent  as  a  result  of  mating 
together  at  some  point  in  the  network  individuals 
genetically  related  to  one  another  in  some  degree. 
Let  us  take  this  as  our  basic  concept  of  inbreeding. 
It  means  that  the  number  of  potentially  different 
germ-to-germ  lines  or  "blood-lines"  concentrated 
in  a  given  individual  animal  is  fewer  if  the 
individual  is  inbred  than  if  it  is  not.  In  other 
words,  the  inbred  individual  possesses  fewer  differ- 
ent ancestors  in  some  particular  generation  or  gen- 


THE  PROBLEM  OF  INBREEDING       105 

erations  than  the  maximum  possible  number  for 
that  generation  or  generations.  This  appears  to  be 
the  most  general  form  in  which  the  concept  of 
inbreeding  may  be  expressed.^  In  whatever  way 
the  mating  of  relatives  is  accomplished,  or  what- 
ever the  degree  of  relationship  of  the  individuals 
mated  together,  the  case  in  last  analysis  comes  back 
to  the  above  statement ;  namely,  that  there  are  ac- 
tually in  the  pedigree  of  the  inbred  individual  fewer 
different  ancestors  in  some  particular  generation  or 
generations  than  the  maximum  possible  number.^ 
The  idea  suggested  in  the  foregoing  paragraph 
may  be  expressed  symbolically  as  follows.  If 
there  is  absolutely  no  collateral  relationship 
between  any  of  the  individuals  in  a  pedigree,  the 
number  of  different  individuals  in  succeeding 
ancestral  generations  will  be  given  by  the  series 

X  <-->  (1)  2  <->(2)  4  <-^  (3)  8  <r^  (4)  16  <r^ 

(5)  32  <~>  (n)  2  %  (i) 

where    the    numbers    in    parenthesis    denote    the 
numbers  of  the  ancestral  generations  (1  =  parents, 

^  This,  of  course,  looks  at  the  matter  primarily  from  the  standpoint 
of  kinship.     This  is  all  that  is  intended  here. 

2  This  generalized  concept  of  inbreeding  seems  to  me  to  be  in 
essential  (though  not  entirely  in  verbal)  agreement  with  that  of  O.  F. 
Cook,  whose  interesting  general  discussions  of  this  and  related  prob- 
lems are  summarized  in  a  recent  paper  ("The  Superiority  of  Line 
Breeding  over  Narrow  Breeding,"  U.S.  Dept.  Agr.,  Bur.  Plant  Ind. 
Bui.  146,  1909).  I  use  "inbreeding"  as  a  generic  term,  while  Cook 
regards  it  as  a  species  of  "line  breeding."  This  seems  to  me  to  be  a 
purely  terminological  difference,  and  not  of  great  consequence. 


106    MODES  OF  RESEARCH  IN  GENETICS 

2  =  grandparents,  3  =  great-grandparents,  and  so 
on),  and  the  free  figures  denote  the  maximum 
possible  number  of  different  ancestors  to  the 
indicated  generation.  If  in  any  generation  in  the 
series  relatives  are  bred  together,  the  same  indi- 
vidual will  appear  more  than  once  in  the  ancestral 
series,  and  the  number  of  different  individual 
ancestors  in  the  higher  terms  will  be  accordingly 
diminished  below  the  maximum  number  as  given 
in  (i).     The  series  will  then  become 

X  <-->  (1)2  <->  (2)4  -  2/1  <->  (3)8  -  2/2  <-^  (ii) 

(4)16  -  2/3  <->  (5)32  -2/4.  .  ., 

where  2/1,  2/2>  2/3>  •  •  •  may,  in  the  nth  generation, 
have  any  value  not  greater  than  2"  —  2,  in  the 
case  of  organisms  in  which  two  individuals  must 
cooperate  in  the  process  of  reproduction.  The 
final  limiting  case  is,  of  course,  self-fertilization, 
where  the  number  of  ancestors  reduces  to  1  in  each 
generation. 

The  Measurement  of  the  Degree  of  In- 
breeding 

This  brings  us  to  a  consideration  of  a  practical 
and  general  measure  of  the  degree  of  inbreeding 
exhibited  in  a  particular  pedigree.  This  problem 
has  been  attacked  by  a  number  of  investigators, 
but  so  far  as  I  have  been  able  to  learn  all  previous 
measures  have  been  modifications  in  one  form  or 


THE  PROBLEM  OF  INBREEDING       107 

another  of  the  scheme  of^  Lehndorff.  This  plan  ^ 
took  account,  as  a  measure  of  inbreeding,  only  of 
the  number  of  generations  intervening  between 
that  generation  in  which  relatives  were  bred 
together,  and  that  generation  in  which  their  first 
common  ancestor  was  found.  Thus  Lehndorff 
says : ^ 

"I  am  of  opinion,  that  a  horse  should  only  be 
termed  in-bred,  when  in  sum  total  less  than  four 
degrees  lay  between  its  parents  and  their  common 
ancestor;  in  other  words,  when  the  children  or 
grandchildren  of  a  stallion  or  a  mare  are  mated,  I 
call  their  produce  in-bred;  but  this  term  does  not 
apply  to  the  produce  of  great-grandchildren  of  the 
common  ancestor.  We  must  not  forget  that  in 
the  pedigrees  of  horses  the  word  brother  or  sister 
often  means  half-brother  or  half-sister,  and  that 
here  the  definition  borrowed  from  the  human 
family  connection  is  not  applicable. 

"As  breeding  within  moderate  relationship  I 
reckon  the  mating  of  stallion  and  mare  that  are 
removed  from  their  common  ancestor  four,  five,  or 
six  degrees.  It  is  indifferent  whether  they  are  on 
both  sides  equidistant  from,  or  one  of  them  nearer 
to  the  male  or  female  progenitor  than  the  other." 

Von  Oettingen  used  a  measure  exactly  the  same 
in  principle  as  this  of  Lehndorff's.     The  system  of 

^  Cf.  Lehndorff,  G.  "Horse-breeding  Recollections,"  Phila- 
delphia, 1887. 

'  Loc.  cU.,  p.  49. 


108    MODES  OF  RESEARCH  IN  GENETICS 

Bruce  Low,  though  somewhat  differently  stated, 
comes  to  essentially  the  same  thing,  so  far  as  I 
am  able  to  determine  from  abstracts,  this  author's 
original  writings  not  having  been  accessible  to  me. 

All  systems  based  on  the  number  of  "free 
generations"  alone  do  not  furnish  a  precise  or 
reliable  measure  of  the  real  intensity  of  inbreeding. 
The  essential  reason  for  this  failure,  stated  baldly* 
is  that  they  do  not  take  account  of  the  composition 
of  the  generation  to  which  the  **  common  ances- 
tors "  of  an  inbred  pair  belong. 

In  developing  a  general  measure  of  the  intensity 
of  inbreeding  we  may  well  start  from  the  con- 
ception set  forth  in  the  preceding  section ;  namely, 
that  the  inbred  individual  possesses  fewer  different 
ancestors  than  the  maximum  possible  number. 
Besides  this  factor  account  must  be  taken  of  the 
generation  or  generations  in  which  the  reduced 
number  of  different  ancestors  is  found,  and  the 
extent  to  which  these  generations  are  removed 
(in  the  sense  of  Lehndorff  discussed  above)  from 
the  individual  or  generation  under  consideration. 
In  other  words,  the  two  factors  which  must  be 
included  in  a  general  measure  of  the  intensity  of 
inbreeding  are  (a)  the  amount  of  ancestral  reduc- 
tion in  successively  earlier  generations,  and  (6)  the 
rate  of  this  reduction  over  any  specified  number  of 
generations. 

Both  of  these  demands  are  met,  I  think,  by 
taking  as  a  measure  of  the  intensity  of  inbreeding 


THE  PROBLEM  OF  INBREEDING       109 

in  any  generation  the  proportionate  degree  to 
which  the  actually  existent  number  of  different 
ancestral  individuals  fails  to  reach  the  maximum 
possible  number,  and  by  specifying  the  location 
in  the  series  of  the  generation  under  discussion. 
The  statement  is  amplified  and  made  more 
precise  in  the  following  propositions : 

1.  The  production  of  the  individual  must  be 
the  point  of  departure  in  any  analytical  considera- 
tion of  inbreeding,  leading  towards  its  measure- 
ment. That  is,  the  question  to  which  one  wants 
an  answer  is :  What  degree  of  inbreeding  was 
involved  in  the  production  of  this  particular 
animal  ? 

2.  It  is  therefore  necessary  practically  to  start 
with  the  individual  and  work  backwards  into  the 
ancestry  in  measuring  the  inbreeding,  rather  than 
to  start  back  in  the  ancestry  and  work  down 
towards  the  individual. 

3.  In  the  genetic  passage  from  the  n  +  1th 
generation  to  the  nth,  or  in  other  words  the  con- 
tribution of  the  matings  of  the  ?i  +  1th  generation 
to  the  total  amount  of  inbreeding  involved  in  the 
production  of  an  individual,  the  degree  of  inbreed- 
ing involved  will  be  measured  by  the  expression, 

Pn+l  (ill) 

where  2?n+i  denotes  the  maximum  possible  num- 
ber   of    different    individuals    involved    in    the 


no    MODES  OF  RESEAKCH  IN  GENETICS 

matings  of  the  n  +  1  generation,  and  Qn+i  the  ac- 
tual number  of  different  individuals  involved  in 
these  matings.  Z„  may  be  called  a  coefficient  of 
inbreeding.  If  the  value  of  Z  for  successive  gen- 
erations in  the  ancestral  series  be  plotted  to 
the  generation  numbers  as  a  base,  the  points  so 
obtained  will  form  a  curve  which  may  be  des- 
ignated as  the  curve  of  inbreeding. 

It  will  be  noted  that  the  coefficient  of  inbreeding 
Z  is  the  percentage  of  the  difference  between  the 
maximum  possible  number  of  ancestors  in  a  given 
generation,  and  the  actual  number  realized,  in  the 
former.  The  coefficient  may  have  any  value 
between  0  and  100.  When  there  is  no  breeding 
of  relatives  whatever  (that  is,  in  the  entire  absence 
of  inbreeding),  its  value  for  each  generation  is  0. 
As  the  intensity  of  the  inbreeding  increases,  the 
value  of  the  coefficient  rises. 

4.  The  above  measure  of  inbreeding  has  to  do 
primarily  with  the  relationship  aspect  of  the 
problem. 

5.  Since  the  only  possible  infallible  criterion  of 
relationship  between  individuals  is  common  an- 
cestry in  some  earlier  generation,  we  are  led  to  the 
practical  rule,  in  measuring  the  degree  of  inbreed- 
ing in  a  pedigree,  to  regard  all  different  individuals 
as  entirely  unrelated  until  the  contrary  is  proved 
by  the  finding  of  a  common  ancestor.  This  no 
doubt  appears  at  this  stage  of  the  discussion  as  an 
exceedingly  obvious  truism.     The  reader  is  urged 


THE  PROBLEM  OF  INBREEDING       111 

to  accept  it  as  such,  and  hold  fast  to  it,  because 
it  will  help  him  over  some  apparent  paradoxes 
later. 

The  method  of  calculating  coefficients  of  in- 
breeding, and  their  real  significance,  will  be  made 
much  clearer  by  the  consideration  of  illustrative 
examples  of  their  application.  To  these  we  may 
therefore  turn. 


The   Calculation   of   Coefficients  of  In- 
breeding 

We  may  first  consider  some  simple  hypothetical 
pedigrees,  before  attacking  the  more  complicated 
ones  actually  realized  in  stock-breeding. 


ILLUSTRATION    I.      CONTINUED    BROTHER    X  SISTER 

BREEDING 

Let  US  begin  with  the  most  extreme  type  of 
inbreeding  possible ;  namely,  the  mating  of  brother 
with  sister  for  a  series  of  generations.  Pedigree 
Table  III  gives  the  pedigree  of  an  individual  so 
bred. 

Let  us  now  proceed  to  the  calculation  of  the 
coefficients  of  inbreeding,  Zo,  Zi,  Z2,  and  Z3. 
For  Zo  we  have 

g  =  2, 


m    MODES  OF  RESEARCH  IN  GENETICS 


PEDIGREE  TABLE  I.     (Hypothetical) 

To  Illustrate  the  Breeding  of  Brother  x  Sister,  out 
OF  Brother  X  Sister,  Continued  for  a  Series  of 

Generations 


X 


Ancestral  Generation 


a 


d 


d 


2 


1/ 


/ 


1/ 


1/ 


g 
h 


9 
h 


g 
h 

g 
h 


9 
h 


'9 

k 


h 


g 
h 


whence 


Zo  = 


100  (0) 

2 


=  0. 


THE  PROBLEM  OF  INBREEDING      113 

In  the  same  way, 

Z.  =  l-M^)  =  50. 


Z.  =  100^  =  75. 

o 

_  100  (16-2)   _ 
16 


These  results  may  be  expressed  verbally  in  the 
following  way :  In  the  last  two  ancestral  genera- 
tions X  is  50  per  cent  inbred;  in  the  last  three 
generations  it  is  75  per  cent  inbred ;  and  in 
the  last  four  generations  it  is  87.5  per  cent 
inbred. 

This  pedigree  table  and  the  constants  will 
repay  further  consideration,  since  the  case  is  a 
limiting  one.  With  the  table  at  hand  it  is  possible 
to  grasp  a  little  more  clearly  the  precise  meaning 
of  the  coefficients  of  inbreeding.  Thus  it  is  seen 
that  what  the  value  of  Z\  =  50  really  signifies 
is  that  because  the  individuals  a  and  h  were 
brother  and  sister  the  number  of  different  ancestors 
which  X  can  possibly  have  in  any  ancestral  genera- 
tion cannot  be  more  than  50  per  cent  of  the  total 
number  theoretically  possible  for  the  generation. 
That  is,  ir's  sire  and  dam  having  been  brother  and 
sister  means  that  x  cannot  have  had  more  than 
2048  different  great-great-great-great-great-great- 


114    MODES  OF  RESEARCH  IN  GENETICS 

great-great-great-grandparents,  instead  of  the 
possible  4096.  He  may  have  had  fewer  than 
2048,  but  Zi  =  50  tells  us  that  he  could  not  have 
had  more.  Similarly,  Zi  =  75  indicates  that  since 
c  and  d,  the  grandsire  and  granddam  of  x,  were 
brother  and  sister,  x  cannot  have  in  any  earlier 
ancestral  generation  more  than  25  per  cent  of  the 
theoretically  possible  number  of  ancestors  for 
that  generation.  And  so  on  for  the  other  values 
of  Z. 

In  the  limiting  case  of  the  closest  inbreeding 
possible  the  successive  Z's  will  have  the  values 
given  in  the  table  on  the  opposite  page. 

From  this  table  it  is  apparent  that  while  the 
narrowing  or  exclusion  of  the  possible  different 
source  lines  of  descent  proceeds  very  rapidly  in 
the  first  few  generations  of  brother  X  sister  breed- 
ing, only  relatively  little  change  is  made  by  further 
generations  of  this  sort  of  breeding.  Thus  in 
seven  generations  of  brother  X  sister  breeding  all 
but  about  1.5  per  cent  of  the  potentially  different 
ancestral  *' blood  lines"  will  have  been  eliminated. 
After  16  generations  of  this  sort  of  breeding  (a 
number  easily  attainable  in  ordinary  breeding 
experiments)  an  individual  so  bred  can  by  no 
chance  possess  more  than  yoVo  ^^  one  per  cent 
of  the  different  lines  of  ancestral  descent  which  are 
theoretically  possible.  This  table  strongly  sug- 
gests that  if,  in  an  experiment  to  test  the  influence 
of   inbreeding,    no   particular   effect   is   observed 


THE  PROBLEM  OF  INBREEDING      115 


TABLE  1 

Values  of  the  Successive  Coefficients  of  Inbreeding 
(Zo  to  Zis)   IN  the  Case  of  the  Most  Intense  In- 
breeding    Possible      (Brother  X  Sister     out     of 
Brother  X  Sister  —  Continued) 


Coefficient  of 
Inbreeding 

Ancestral  Genera- 
tions Included 

Numerical  Value  of 
Coefficient 

Zo 

1 

0 

Zi 

2 

50 

Z^ 

3 

75 

Zz 

4 

87.5 

z. 

5 

93.75 

z. 

6 

96.875  1 

z. 

7 

98.4375 

Zt 

8 

99.21875 

Zs 

9 

99.609375 

Z9 

10 

99.8046875 

Zio 

11 

99.90234375 

Zn 

12 

99.951171875 

Z12 

13 

99.9755859375 

Zi3 

14 

99.98779296875 

Zi4 

15 

99.993896484375 

Zl5 

16 

99.9969482421875 

during  ten  generations  of  brother  X  sister  breeding, 
it  is  extremely  improbable  that  any  effect  will  be 


^  There  is,  of  course,  no  further  point  in  the  retention  of  all  the 
decimals  in  these  coefficients  than  to  make  plain  the  law  of  their 
formation.  In  the  case  of  maximum  inbreeding  here  illustrated,  the 
Z's  are  the  successive  terms  of  a  series  in  which  any  term  is  equal 
to  the  preceding  term  plus  one  half  the  difference  between  the  pre- 
ceding term  and  100,  or  in  which  the  successive  differences  are  halved. 


116    MODES  OF  RESEARCH  IN  GENETICS 

produced  by  a  further  continuation  of  the  same 
method  of  breeding.  If  an  apparent  effect  should 
suddenly  appear  some  time  later  than  the  tenth 
generation,  the  case  would  need  the  most  critical 
scrutiny,  to  determine  whether  the  observed 
effect  had  really  been  due  to  the  inbreeding,  rather 
than  to  some  other  unsuspected  cause. 

The  values  of  the  Z's  in  Table  I  are  maxima. 
No  particular  coefficient  of  inbreeding  can  have  a 
higher  value  than  that  given  in  the  table.  It  is 
not  possible,  for  example,  so  to  breed  any  animal 


100 
80 

/? 

^' 

♦a     6U 

1 

s 

/ 

7 

1 

O    40 

20 
n 

/     i 
1    1 

/!  / 
1 ' 

1    1 

\l 
1/ 

1  / 

i 

i             i 

[          ( 

Gener 

i              1 
atious 

[)              1 

2               1 

1 

Fig.  1.  Curves  of  inbreeding,  showing  (a)  the  limiting  case  of  con- 
tinued brother  X  sister  breeding,  wherein  the  successive  coefficients  of 
inbreeding  have  the  maximum  values ;  (b)  continued  parent  X  off- 
spring mating ;  (c)  continued  first-cousin  X  first-cousin  mating  where 
the  cousinship  is  double  (C^  X  C^),  and  (d)  continued  first-cousin 
X first-cousin  mating  where  the  cousinship  is  single  (C^  X  CO-  The 
continued  mating  of  uncle  X  niece  gives  the  same  curve  as  C^  X  C^ 


THE  PROBLEM  OF  INBREEDING      117 

(having  an  obligate  bisexual  type  of  reproduc- 
tion) that  its  pedigree  on  analysis  will  give 
Z3>87.5.  If,  therefore,  the  coeflScients  of  Table 
I  are  plotted,  the  result  will  be  the  maximum 
limiting  curve  of  inbreeding.  This  curve  is  shown 
in  Fig.  1. 

In  all  actually  realized  pedigrees  except  those  in 
which  there  has  been  continued  brother  X  sister 
breeding  the  curve  of  inbreeding  found  will  lie 
wholly  or  in  part  below  the  maximum  curve 
shown  in  Fig.  1. 

ILLUSTRATION  II.     PARENT  X  OFFSPRING  BREEDING 

The  next  illustration  of  the  application  of 
coefficients  of  inbreeding  will  be  the  general  case 
of  back-crossing,  that  is,  the  mating  of  parent 
X  offspring.  Such  a  case  is  illustrated  in  the 
hypothetical  pedigree.  Table  II. 

Here  it  will  be  seen  that  6,  the  dam  of  y,  is  a 
daughter  of  a,  who  is  also  the  sire  of  y,  and  that  in 
each  preceding  generation  every  daughter  is  bred 
back  to  her  sire.  Proceeding  as  before  to  calculate 
the  coefficients  of  inbreeding,  we  have,  first, 

y         _100     (2-2)     _     ^ 

Zo-  -  -0. 

In  forming  the  expression  for  Zi  we  are  met 
by  the  fact  in  determining  ^n+i  for  generation  2 
that  the  individual  a  has  already  appeared  once 
and  been  counted  as  a  "different"  ancestor  in 


118    MODES  OF  RESEARCH   IN  GENETICS 


PEDIGREE  TABLE  U     (Hypothetical) 
To  Illustrate  the  Breeding  of  Parent  X  Offspring 


Generation  number    . 


d 

< 

7 

a 

* 

.9 
d 

.e 

< 

.  i 

i 

u 

a 

< 

.e 

[b 

i 

f 

a 

c 

- 

> 

1 

2 

,      N 

3 

n 
J 

7 

.9 
'd 

7 

^9 
'd 


d 

e 

a 

s 


generation  1.     Therefore  it  will  not  be  counted 
a  second  time  in  generation  2,  and  we  have 

^100(4-3)^ 
4 


THE  PROBLEM  OF  INBREEDING       119 

and  by  the  same  process, 

Z.  =  MiSri)  =  50, 

o 

Z3=M0i^=  68.75. 
16 

and  so  forth. 

The  values  of  the  successive  coeflScients  for 
parent  X  offspring  for  16  ancestral  generations  are 
given  in  Table  2. 

By  comparison  of  this  table  with  Table  1  it  is 
evident  that  while  the  increase  in  intensity  of 
inbreeding  is  not  so  rapid  in  the  first  few  ancestral 
generations  by  this  parent  X  offspring  type  of 
breeding  as  with  the  brother  X  sister  type,  by  the 
time  the  tenth  ancestral  generation  is  reached  the 
values  are  for  practical  purposes  the  same. 

The  curve  of  inbreeding  for  continued  parent 
X  offspring  breeding  is  shown  in  Fig.  1. 


ILLUSTRATION    III.     FIRST-COUSIN    X   FIRST-COUSIN 

BREEDING 

As  a  third  illustration  may  be  taken  the  case  of 
continued  cousin  mating.  Such  breeding  repre- 
sents the  next  step  in  decreasing  intensity  of 
inbreeding  beyond  the   parent  X  offspring  type. 


120    MODES  OF  RESEARCH  IN   GENETICS 

TABLE  2 

Values  of  the  Successive  Coefficients  of  Inbreeding 
IN  THE  Case  of  Continued  Parent  x  Offspring 
Mating 


Coefficient  of 
Inbreeding 

Ancestral  Genera- 
tions Included 

Numerical  Value  of 
Coefficient 

Zo 

1 

0 

Zi 

2 

25 

^2 

3 

50 

^3 

4 

68.75 

Z4 

5 

81.25 

Zs 

6 

89.06 

Ze 

7 

93.75 

Zr 

8 

96.48 

^8 

9 

98.05 

Za 

10 

98.93 

Zio 

11 

99.41 

Zu 

12 

99.68 

^12 

13 

99.83 

Zi3 

14 

99.91 

Zi4 

15 

99.95 

Zi5 

16 

99.97 

There  are,  of  course,  two  possible  sorts  of  first 
cousins,  single  and  double.  In  the  first  case  one  of 
the  parents  of  any  individual  is  a  brother  (or  sister) 
to  one  of  the  parents  of  the  other  individual  in 
the  mating.  In  the  second  case  both  the  parents 
occupy  this  relation  to  the  parents  of  the  other 
individual  in  the  mating. 

These  two  sorts  of  first  cousinship  are  shown  in 
Pedigree  Tables  III  and  IV. 


THE  PROBLEM  OF  INBREEDING       121 

PEDIGREE  TABLE  III     (Hypothetical) 

To  Illustrate  the  Continued  Breeding  of  First-Cousin 
X  First-Cousin  —  Single  Cousins 


< 
[n 

'S 

8 

c 

. 

fi 

\2 

0 

h 

< 

{^ 

a 

. 

Jl 
12 

(m 

< 

1! 

[n 

e 

< 

f 

Jl 
\2 

j 

• 

[r 

f?o 

A 

* 

(m 

s 

9 

< 

/3 
14 

[n 

'd 

i 

8 

f 

0 

b 

< 

h 

< 
[p 

/5 
\6 

im 

Jl 
12 

'k 

< 

8 

[n 

J 

< 

15 

u 

I 

< 

V 

g 

Generation  number       .     . 

1 

2 

3 

4 

5 

^  Owing  to  the  limitation  of  the  alphabet,  resort  is  had  to  numbers 
to  designate  individuals  in  this  generation. 


122    MODES  OF  RESEARCH  IN  GENETICS 

PEDIGREE  TABLE  IV   (Hypothetical) 

To  Illustrate  the  Continued  Breeding  of  First-Cousin 
X  First-Cousin  —  Double  Cousins 


/» 

^ 

(k 

\p 

9 

1 

iv 

c 

' 

.h 

m 

\p 

{n 

V 

a 

< 

r  ■ 

ik 

\p 

I 

< 

d 

< 

1^ 

m 

\P 

J 

In 

{^ 

A2 

- 

\r 

/^ 

r 

ik 

9 

< 

{? 

e 

< 

h 

< 

Jo 

\v 

1' 

\n 

V 

b 

< 

/" 

f  ■ 

\k 

\v 

I 

[i 

{? 

J 

< 

1° 

• 

im 

( 

[J 

< 

1? 

n 

Generation  number       .     . 

1 

2 

3 

4 

5 

The    values    of    the    successive    coefficients    of 
inbreeding  for  these  cases  are  given  in  Table  3. 


THE  PROBLEM  OF  INBREEDING       123 

The  calculation  is  carried  out  in  accordance  with 
the  same  principles  as  have  been  illustrated  in  the 
previous  cases.    We  have,  from  Pedigree  Table  III, 


and 


z,  =  Mi±=l)  =  0, 

4 


since  in  generations  1  and  2  there  are  two  and 
four  different  ancestors  respectively. 

o 

since  in  generation  3  the  two  individuals  g  and  h 
each  appear  twice,  and  by  our  rule  any  ancestor 
is  only  counted  once. 

16 

since  in  generation  4  the  individuals  m  and  n 
appear  four  times  and  are  only  counted  as  different 
ancestors  once  each,  and  individuals  o  and  'p  each 
appear  twice. 

The  data  of  Table  3  are  given  graphically  in 
Fig.  1,  together  with  the  curve  for  brother  X 
sister  and  parent  X  offspring. 

From  the  table  and  figure  it  is  seen  that  with 
continued  inbreeding  according  to  any  one  of  these 
four  types  the  coefficient  approaches  the  value 


124    MODES  OF  RESEARCH  IN  GENETICS 


TABLE  3 

Values  of  the  Successive  Coefficients  of  Inbreeding 
IN  THE  Case  of  Continued  Cousin  Mating 


Coefficient  of 
Inbreeding 

Ancestral  Gen- 
eration Included 

Coefficient  for 
Single  Cousins 

Coefficient  for 
Double  Cousins 

Zo 

1 

0 

0 

Zi 

2 

0 

0 

^2 

3 

25.00 

50.00 

Z^ 

4 

50.00 

75.00 

Z4 

5 

68.75 

87.50 

Z5 

6 

81.25 

93.75 

z. 

7 

89.06 

96.88 

z. 

8 

93.75 

98.44 

Zs 

9 

96.48 

99.22 

Z9 

10 

98.05 

99.61 

Zio 

11 

98.93 

99.80 

Zii 

12 

99.41 

99.90 

Zyi 

13 

99.68 

99.95 

Zi3 

14 

99.83 

99.98 

Zi4 

15 

99.91 

99.99 

Zi5 

16 

99.95 

99.994 

100.  The  rate  of  approach  is  different,  however, 
in  the  different  cases.  The  curves  fall  into  two 
pairs.  The  brother  X  sister  and  the  double  cousin 
curves  are  precisely  alike  so  far  as  concerns  their 
curvature  or  shape  at  any  given  point.  Similarly, 
the  parent  X  offspring  and  single  cousin  curves 
are  of  the  same  shape.  The  essential  point  of 
difference  is  that  the  cousin  curves  lag  a  generation 
behind  the  others. 


THE  PROBLEM  OF  INBREEDING       125 

ILLUSTRATION  IV.    UNCLE    X  NIECE  MATING 

Let  US  now  consider  the  question  of  the  degree 

of  inbreeding  following  continued  matings  of  the 

avuncular  type  of  relationship.     Pedigree  Table 

V  gives  a  pedigree  in  which  each  mating  is  of  uncle 

X  niece. 

From  this  table  it  appears  that  the  values  of  the 
coefficients  of  inbreeding  will  be  exactly  the  same 
for  this  type  of  mating  as  in  the  case  of  single 
cousin  mating.  Or,  in  other  words,  Z's  form  the 
following  series. 


Values  of  Coefficients  of  Inbreeding  for  Continued 

Uncle  X  Niece  Mating 


Coefficient 

Number  of  Ancestral 
Generations 

Value  of  Coefficient 

Zo 

1 

0 

Zi 

2 

0 

z. 

3 

25.00 

z. 

4 

50.00 

z. 

5 

68.75 

z. 

6 

81.25 

etc. 

etc. 

etc.  as  in  Table  3 

From  the  data  presented  it  is  clear  that  in- 
breeding continued  for  about  ten  generations, 
quite  regardless  of  the  type  of  mating  provided 
only  it  be  continuously  followed,  leads  to  within 
one  or  two  per  cent  of  complete  *' concentration  of 


126    MODES  OF  RESEARCH  IN  GENETICS 


PEDIGREE  TABLE   V   (Hypothetical) 
To  Illustrate  the  Mating  of  Uncle  X  Niece 


m 

{.• 

9 

\y 

n 

c 

< 

[n 

(o 

h 

{ 

[p 

a 

< 

r 

9 

[n 

I 

[h 

{; 

- 

d 

< 

f 

[1 

J 

< 

[1 

X 

• 

[n 
ft 

c 

\9 

[h 

e 

< 

{1 

r  • 

X 

d 

< 

i 

• 

{? 

b 

' 

c 

{i 

k 

< 
[d 

f      9 

I 

J 

< 

s 

8 

I 

< 

r 

s 

t 

Generation  number       .     . 

1 

2 

3 

4 

5 

blood."     The    bearing    of    this    result    upon    the 
general  question  of  the  degree  of  inbreeding  which 


THE  PROBLEM  OF  INBREEDING       127 

exists  in  the  ancestry  of  our  domestic  animals 
to-day  is  obvious.  To  consider  but  a  single 
case :  In  1789  ^  a  law  was  passed  prohibiting  the 
importation  of  cattle  into  the  island  of  Jersey. 
Hence  it  follows  that  all  pure-bred  Jersey  cattle 
of  the  present  time  must  be  the  descendants  of 
the  relatively  few  animals  on  the  island  in  1790. 
Taking  three  years  as  about  the  average  generation 
interval  in  cattle,  this  means  about  forty  genera- 
tions since  the  island  was  closed  to  importation. 
The  concentration  of  lines  of  descent  which  must 
have  occurred  in  this  time  merely  by  the  dropping 
of  lines  and  quite  regardless  of  the  type  of  mating 
is  obvious. 

ILLUSTRATION    V.    THE    PEDIGREE    OF    THE    JERSEY 
COW,    BESS   WEAVER    (155121) 

Leaving  now  the  hypothetical  cases,  we  may 
consider  some  pedigrees  of  actually  existing 
animals.  For  a  first  illustration  of  this  sort  the 
Jersey  cow,  Bess  Weaver,  may  be  taken.  Her 
pedigree  through  four  ancestral  generations  is 
shown  in  Pedigree  Table  VI. 

In  the  twelfth  ancestral  generation  the  theo- 
retically possible  number  of  different  ancestors  is 
4096.  In  a  relatively  long  pedigree,  such  as 
arises  in  dealing  with  registered  cattle,  it  would 
obviously   be   an   extremely   tedious   business   to 

^  Teste  Rees's  Encyclopedia  and  H.  S.  Redfield,  Natl.  Stockman 
and  Farmer,  December  15,  1892. 


128    MODES  OF  RESEARCH  IN  GENETICS 


PEDIGREE  TABLE  VI 


o 


> 


03 

n 


(N 


U3 


o 


to 

l-H 

o 
o 

Dh 

M 
M 
O 

> 

Q 

00 

OS 

CO 
lO 

6 

No.  35913  $ 

Sisera's  Stoke 
Pogis 

No.  26271          $ 
Juno's  Stoke  Pogis 

No.  14207               $ 
Alphea's  Stoke  Pogis 

No.  14436                9 
Carlo's  Juno 

No.  37346          9 
Sisera 

No.  1881                  $ 
Duchess  Stoke  Pogis 

No.  6246                  9 
Edith  Darby 

No.  79860  9 
Baltimore 

No.  19350          $ 
Patrick  Fawkes 

No.  10469               $ 
Regal  Koffee 

No.  21574               9 
Kermesse 

No.  17900          9 
Avoca  2nd 

No.  3286                  $ 
Champion's  Son 

No.  17769                9 
Avoca 

No.  126629 

Peg  Weaver                                        +o 

No.  35913   $ 
0 

Sisera's  Stoke 
Pogis 

No.  26271          $ 

X 

Juno's  Stoke  Pogis 

No.  14207               $ 

X 

Alphea's  Stoke  Pogis 

No.  14436                9 
X  Carlo's  Juno 

No.  87346          9 

X 

Sisera 

No.  18811                $ 
X 

Duchess  Stoke  Pogis 

No.  6246                  9 
X     Edith  Darby 

No.  126626  9 
Kate  Weaver 

No.  36382          $ 
General  Kelly 

No.  19350               $ 
0   Patrick  Fawkes 

No.  95606                9 
0     Balm 

No.  95606         9 
Balm 

No.  7056                  $ 
America's  Champion 

No.  95605                9 
Maid  of  Gilead  2nd 

THE  PROBLEM  OF  INBREEDING      129 

determine  the  value  of  q  by  direct  counting,  as  has 
been  done  in  the  preceding  simpler  illustrations. 
The  calculation  of  the  coefficients  of  inbreeding 
may  be  greatly  simplified  in  the  case  of  long  pedi- 
grees by  a  system  of  counting  which  makes  the 
line  of  descent  the  unit  rather  than  the  individual. 
This  system  is  used  in  the  above  pedigree  as  an 
illustration  of  method,  although  only  4  ancestral 
generations  are  here  considered.  While  each 
individual  animal  which  is  eliminated  because  of 
previous  appearances  in  a  lower  ancestral  genera- 
tion is  marked  with  an  X,  those  at  the  apex  of  a 
line  of  descent  are  marked  with  a  cross  within  a 
circle.  These  latter  are  all  that  need  to  be  counted 
directly.  Thus  the  bull  Sisera's  Stoke  Pogis 
first  appears  in  the  second  ancestral  generation 
as  the  sire  of  Davy  Stoke  Pogis.  He  next  appears 
(here  marked  with  a  cross  within  a  circle)  in  the 
same  generation  as  the  sire  of  Peg  Weaver.  He 
will,  by  the  general  rule  of  coefficients  of  inbreed- 
ing, not  be  counted  as  a  "different"  ancestor  the 
second  time  in  this  generation.  But  this  auto- 
matically eliminates  his  two  parents  in  the  third 
ancestral  generation,  his  four  grandparents  in  the 
fourth  generation,  and  so  on  until  in  the  twelfth 
generation  1024  ancestors  of  Sisera's  Stoke  Pogis 
will  be  so  eliminated.  The  same  consideration 
applies  in  every  other  like  case. 

Practically,  then,  the  method  of  dealing  with  a 
pedigree  of  this  sort  is  first  to  go  through  and 


130    MODES  OF  RESEARCH  IN  GENETICS 

indicate  in  a  distinctive  way  every  primary  * 
reappearance  of  individuals.  Then  form  a  table 
on  the  plan  of  Table  4,  the  character  of  which  is 
so  obvious  as  not  to  need  detailed  explanation. 
This  table  is  to  be  read  in  the  following  way : 
Because  of  the  reappearance  of  Sisera's  Stoke 
Pogis  in  the  2d  ancestral  generation  Bess  Weaver 
has  1  fewer  ancestors  in  that  generation  than  she 
would  have  had  in  the  entire  absence  of  inbreed- 
ing; 2  fewer  in  the  3d  generation,  and  so  on. 
The  totals  of  the  columns  of  this  table  are  the 
values,  for  each  generation,  of 

in  (i).  These  totals,  multiplied  by  100,  have  then 
merely  to  be  divided  by  p^+i  in  order  to  obtain 
the  successive  Z's.  The  whole  operation  may  be 
very  quickly  carried  out.  It  is  not  necessary, 
in  fact,  to  fill  out  the  whole  of  the  later  columns 
of  the  table;  the  entries  may  be  cumulated. 
For  the  present  pedigree  we  have 

Zo  =  0,  as  always.2 

Zi  = —  =  25  per  cent, 

1  By  "primary"  reappearance  in  the  pedigree  is  meant  a  reap- 
pearance as  the  sire  or  dam  of  an  individual  which  has  not  itself 
appeared  before  in  the  lower  ancestral  generations.  Thus  Patrick 
Fawkes  makes  a  'primary  reappearance  in  the  fourth  ancestral  genera- 
tion as  the  sire  of  General  Kelly,  a  bull  which  is  not  found  in  any 
generation  below  the  third. 

2  The  apparent  paradox  implied  in  the  fact  that  Zq  must  always 


THE  PROBLEM  OF  INBREEDING       131 


TABLE  4 

Working  Table  used  in  Calculating  the  Coefficients 
OF  Inbreeding  for  Pedigree  Table  VI 


Animal. 

Ancestral  Generation. 

2 

3 

4 

Sisera's  Stoke  Pogis  . 
Patrick  Pawkes     .... 
Balm 

1 

2 

4 
1 
1 

Totals 

1 

2 

6 

Z^  = 


100(2) 
8 


=  25  per  cent, 


Z,  =  IM?)  =  37.5  per  cent. 
16 

From  these  values  it  is  seen  that  in  the  first  four 
ancestral  generations  the  cow  Bess  Weaver  is 
37.5  per  cent  inbred.  This  is  a  perfectly  definite 
figure,  directly  comparable  with  similar  constants 
for  other  animals.  Of  course,  if  we  were  to  go 
back  more  generations  we  should  find  Bess  Weaver 
still  more  inbred,  that  is,  the  coefficients  would 


be  zero,  or  in  other  words  that  in  the  first  ancestral  generation,  con- 
sidered alone,  there  is  no  inbreeding  will  be  cleared  up,  if  it  strikes 
the  reader  as  paradoxical,  by  a  reconsideration  of  the  general  prin- 
ciple numbered  5  on  p.  110.  The  point  of  course  is  that  it  is  impos- 
sible to  say  whether  the  parents  are  or  are  not  related  to  one  another 
until  something  is  known  of  their  parentage,  or  in  other  words,  until 
a  second  ancestral  generation  is  considered. 


132    MODES  OF  RESEARCH  IN  GENETICS 

grow  larger  with  each  case  of  the  mating  of  rela- 
tives. Since  the  case  is  cited  here  merely  for 
illustration  of  method,  four  generations  only  are 
considered. 

II.    Inbreeding  and   Relationship  Coeffi- 
cients 

In  the  discussion  which  has  preceded  no 
mention  has  been  made  of  an  important  con- 
sideration which  arises  in  connection  with  the 
analysis  of  inbreeding  by  means  of  the  coeflBcients 
described.  This  further  problem,  to  which  we 
may  now  turn,  may  be  stated  in  the  following 
way : 

The  pedigree  of  an  individual  consists  of  two 
halves.  One  of  these  halves  is  made  up  of  the 
sire  and  his  ancestors ;  the  other  of  the  dam 
and  her  ancestors.  Following  the  conception  of 
inbreeding  set  forth  in  detail  in  the  earlier 
papers  of  this  series,  it  is  plain  that  the  values 
of  the  coeflBcients  of  inbreeding  for  a  particular 
pedigree  are  composed  of  the  following  ele- 
ments : 

1.  The  occurrence  of  the  same  individual 
animals  more  than  once  on  the  sire's  side  of  the 
pedigree  only. 

2.  The  occurrence  of  the  same  individual 
animals  more  than  once  on  the  dam's  side  of  the 
pedigree  only. 

3.  The  reappearance  of  animals  which  appear 


THE   PROBLEN  OF  INBREEDING        133 

first  on  one  side  of  the  pedigree  (either  the  sire's 
or  the  dam's)  then  on  the  other  side. 

If  only  1  and  2  are  to  be  found  in  the  pedigree,  it 
means  that  the  sire  and  the  dam  are  totally  un- 
related (within  the  limits  covered  by  the  pedigree 
in  the  particular  case).  On  the  other  hand,  the 
occurrence  of  3  means  that  sire  and  dam  are  in 
some  degree  related,  and  that  a  portion  of  the 
observed  inbreeding  arises  because  of  that  fact. 
Now  the  coeflScients  of  inbreeding,  in  and  of 
themselves,  tell  nothing  about  what  proportionate 
part  has  been  played  by  these  three  elements  in 
reaching  the  final  result.  It  is  a  matter  of  great 
importance  to  have  information  on  this  point, 
because  of  its  genetic  significance.  It  is  now  pro- 
posed to  describe  a  general  method  for  obtaining 
this  desired  information. 

The  first  step  in  the  method,  stated  briefly,  is  to 
break  up  the  pedigree  elimination  table  formed 
to  get  the  successive  values  of  Pn+u  in  our  for- 
mer notation,  into  four  different  parts.  One  of 
these  parts  will  include  the  primary  reappearance 
on  the  sire's  side  of  the  pedigree  of  such  animals 
as  appear  first  on  the  same  side.  This  may  be 
called  the  "male  only"  table.  The  second  part 
will  include  the  primary  reappearance  on  the 
dam's  side  of  such  animals  as  first  appear  on  the 
same  side.  This  is  the  "female  only"  table. 
The  third  part  will  include  the  primary  reappear- 
ance on  the  dam's  side  of  such  animals  as  first 


134    MODES  OF  RESEARCH  IN  GENETICS 

appear  on  the  sire's  side.  The  fourth  part  is  the 
reverse  of  the  third.  These  last  two  may  be  called 
the  "cross  tables."  The  sums  of  the  totals  of 
these  partial  tables  will  give  the  total  p^+i  —  Qn+i 
values  for  the  successive  generations. 

The  formation  of  the  tables  on  this  plan  may  be 
illustrated  with  some  examples.  These  examples 
will  also  show  the  skeleton  method  of  writing 
pedigree  elimination  tables,  which  saves  much 
labor.  It  consists  simply  in  doubling  the  total 
of  the  column  for  each  generation  rather  than  the 
separate  items. 

The  pedigree  for  12  ancestral  generations  of  the 
Jersey  bull  King  Melia  Rioter  14th  (103901)  may 
be  taken  as  the  first  illustration. 

From  these  tables  it  is  obvious  that  a  very  con- 
siderable portion  of  the  inbreeding  shown  in  the 
pedigree  of  King  Melia  Rioter  14th  arises  from  the 
fact  that  his  sire  and  dam  were  closely  related. 
Furthermore,  both  sire  and  dam  are  closely  inbred 
in  their  own  lines.  The  curve  of  total  inbreeding 
in  this  case  is  shown  in  Fig.  2,  along  with  the 
curves  for  continued  brother  X  sister,  and  parent 
by  offspring. 

Table  7  is  clearly  the  one  which  demands  special 
attention.  As  will  shortly  appear,  it  is  the  most 
important  for  the  theory  of  inbreeding.  Let 
us  attempt  its  analysis.  Just  what  does  the  first 
entry  mean  genetically.^  It  states  that  King 
Melia  Rioter,  an  animal  which  first  appeared  on 


THE   PROBLEM  OF  INBREEDING       135 


TABLE  5 

Partial  Pedigree  Elimination  Table  for  King  Melia 
Rioter  14th,  Showing  the  Primary  Reappearances 
ON  the  Sire's  Side  of  the  Pedigree  of  Animals 
which  first  Appear  on  that  Side 


Generation 


Melia  Ann's  Son    . 
Melia  Ann  3d    .     . 
Lucy's  Stoke  Pogis 
Melia  Ann    .     .     . 
St.  Lambert  Boy   . 
Letty  Rioter 
AUie  of  St.  Lambert 
Lord  Aylmer 
Amelia  2d     .     .     . 
Victor  Hugo 
Oakland's  Nora 
Stoke  Pogis  3d  .     . 
Bachelor  of  St  Lam- 
bert 


of 


St. 


Sir   George 
Lambert    . 

Diana's  Rioter 

Orloff  .     .     . 

Lome  .     .     . 

Hugo's  Victoria 

Victor  Hugo 

Pauline     . 

Canada's  John  Bull 

Oakland's  Nora 

Stoke  Pogis  3d 

Kathleen     of     St 
Lambert    . 

Lord  Lisgar 

Lucy  of  St.  Lambert 

Diana  of  St.  Lambert 

Pet  of  St.  Lambert 

Orloff 

Bachelor  of  St.  Lam- 
bert   


3  4 


(2)1 
1 


(6)1 
3 
2 


(32)1 
1 
1 
1 


(82)1 
1 
1 
1 
1 
7 

1 
4 
2 
1 
1 
1 


>10 


11 


12 


^  In  this  and  the  following  tables  the  numbers  in  brackets  are  in 
each  case  twice  the  sum  of  the  numbers  in  the  preceding  column. 
They  represent  the  accumulated  ancestral  reduplication  up  to  the 
generation  in  question. 


136    MODES  OF  RESEARCH  IN  GENETICS 


TABLE  5  —  Continued 

Partial  Pedigree  Elimination  Table  for  King  Melia 
Rioter  14th,  Showing  the  Primary  Reappearances 
ON  THE  Sire's  side  of  the  Pedigree  of  Animals 
WHICH  FIRST  Appear  on  that  Side 


Generation 

Ida  of  St.  Lambert 
Victor  Hugo  . 
Stoke  Pogis  3d  . 
Lord  Lisgar   . 
Lome    .... 
Amelia       .     .     . 
Lord  Lisgar  . 
Pride  of  Windsor 
Laval    .... 
Amelia       .     .     . 
Victor  Hugo 
Laval    .... 
Amelia 

Lisette       .     .     . 
Berthe       .     .     . 


Totals 


16 


41 


8 


105 


(210)1 
2 
2 
3 
1 
1 


219 


10 


(438)1 
1 
2 
1 
2 
3 


447 


11 


(894)1 
1 
1 
1 
1 


898 


12 


1,796 


TABLE   6 

Partial  Pedigree  Elimination  Table  for  King  Melia 
Rioter  14th,  Showing  the  Primary  Reappearances 
on  the  Dam's  Side  of  the  Pedigree  of  Animals 
which  first  Appear  on  that  Side 


Generation 

2 

3 

4 

5 

6 

2 

7 

4 

8 

8 

9 

16 

10 

32 

11 

63 

12 

King's  Rioter  Lad 

1 

128 

1  In  this  and  the  following  tables  the  numbers  in  brackets  are  in 
each  case  twice  the  sum  of  the  numbers  in  the  preceding  column. 
They  represent  the  accumulated  ancestral  reduplication  up  to  the 
generation  in  question. 


THE  PROBLEM  OF  INBREEDING       137 

the  sire's  side  of  the  pedigree,  reappeared  in  the 
second  ancestral  generation  on  the  dam's  side. 
What  this  clearly  means  is  that  at  least  one  half 
of  all  the  dam's  ancestors,  in  the  third  and  higher 
ancestral  generations,  are  identically  the  same 
animals  as  are  ancestors  of  the  sire.     The  next 


to 

(S 


o 
O 


Tflf) 

?'^y 

—  — 

) 

QA 

jv«=5 

)-— 0-— ( 

80 

fl 

CU 

/ 

fi 

/ 

40 

/, 

11/ 

1 

r 

2U 

I 

1 

1 

0 

\ 

6  8  10 

Generations 


12 


14 


Fig.  2.  —  Diagram  showing  (a)  the  total  inbreeding  (heavy  solid 
line)  and  (6)  the  relationship  (heavy  broken  line)  curves  for  the 
Jersey  Bull,  King  Melia  Rioter  14th.  The  high  order  of  the  inbreed- 
ing and  relationship  between  the  sire  and  dam  in  this  case  is  evident 
by  comparison  with  the  lighter  lines,  which  give  the  maximum  values 
for  continued  brother  X  sister  and  parent  X  offspring  breeding. 


entry  in  Table  7  indicates  that  in  the  fourth  and 
higher  ancestral  generations  at  least  f  of  all  the 
dam's  ancestors  were  the  same  individual  animals 
as  were  also  ancestors  of  the  sire.  One  half  of 
them  were  the  same  before  the  reappearance  of 


138    MODES  OF  RESEARCH  IN  GENETICS 

St.   Lambert's  Rioter  King.     He  makes  up  the 
additional  J  of  the  dam's  ancestry. 

TABLE  7 

Partial  Pedigree  Elimination  Table  for  King  Melia 
Rioter  14th,  Showing  the  Primary  Reappearances 
ON  THE  Dam's  Side  of  the  Pedigree  of  Animals 
WHICH  first  Appear  on  the  Sire's  Side. 


Generation 


King  Melia  Rioter   . 
St.  Lambert's  Rioter 

King 

King  of  St.  Lambert 
St.  Lambert  Boy 
St.  Lambert  Boy- 
Oakland's  Nora   .     . 
St.  Lambert's  Rioter 

King 

St.  Lambert  Boy 
King  of  St.  Lambert 
St.  Lambert's  Letty 
Letty  Coles  2d  .  . 
King  of  St.  Lambert 
Louise's  Grace     .     . 


Totals 


2 

1 

3 

(2) 

4 

(4) 
1 

5 

5 

(10) 
1 
1 

12 

6 

(24) 
2 
1 

1 
28 

7 

(56) 
1 
1 

1 

59 

8 

9 

10 

480 

960 

(118) 

1 

(238) 
1 
1 

1 

2 

119 

240 

12 


1,920 


TABLE  8 

Summarized    Pedigree    Elimination    Table    for    King 

Melia  Rioter  14th 


Generation 

2 

1 
1 

3 

2 

4 

6 

6 

7 

41 

4 

59 

104 

8 

105 

8 

119 

9 

219 

16 

240 

10 

11 

12 

^  only     .     . 

9  only     .     . 

Cross  .     .     . 

1 

5 

3 

1 

12 

16 

2 
28 

447 

32 

480 

898 

64 

960 

1,796 

128 

1,920 

Together 

2 

6 

16 

46 

232 

475 

959 

1,922 

3,844 

THE  PROBLEM  OF  INBREEDING       139 

From  this  we  have,  for  the  inbreeding  coeflB- 

cients,  „ 

Zo    =    0 

Zi    =  25.00 

Z2    =  25.00 

Zz    =  37.50 

Z4    =  50.00 

Z5    =  71.88 

Zg    =  81.25 

Z7    =  90.63 

Zs    =  92.77 

Z9    =  93.65 

Zio  =  93.85 

Zii  =  93.85 

These  facts  will  possibly  be  made  clearer  to 
those  not  actually  working  much  with  pedigrees 
by  Table  VII,  which  gives  the  first  four  ancestral 
generations  ^  of  the  pedigree  of  King  Melia  Rioter 
14th. 

Generalizing  the  above  reasoning  we  get  the 
following  result : 

In  A3,  and  higher  ancestral  generations,  f  = 
50.00  per  cent  of  the  dam's  ancestors  are  animals 
which  are  also  ancestors  of  the  sire. 

*  In  the  study  of  pedigrees  stress  is  naturally  laid  on  the  ancestral 
generations,  rather  than  on  the  filial,  as  in  breeding  experiments. 
It  becomes  very  convenient  to  have  a  brief  designation  for  ancestral 
generations,  in  the  same  way  that  Fi,  F2,  etc.,  are  used  to  denote 
filial  generations.  I  would  suggest  the  use  of  the  letter  A  with  sub- 
numbers  for  this  purpose.  We  then  have  Ai  denoting  the  parental 
generation,  A2  the  grandparental,  Az  the  great-grand-parental,  etc. 


140    MODES  OF  RESEARCH  IN  GENETICS 

In  Ai,  and  higher  ancestral  generations,  f  = 
62.50  per  cent  of  the  dam's  ancestors  are  animals 
which  are  also  ancestors  of  the  sire. 

In  A  5,  and  higher  ancestral  generations,  ^|  = 
75.00  per  cent  of  the  dam's  ancestors  are  animals 
which  are  also  ancestors  of  the  sire. 

In  A  6,  and  higher  ancestral  generations,  f|  = 
87.50  per  cent  of  the  dam's  ancestors  are  animals 
which  are  also  ancestors  of  the  sire. 

In  A7,  and  higher  ancestral  generations,  f|  = 
92.19  per  cent  of  the  dam's  ancestors  are  animals 
which  are  also  ancestors  of  the  sire. 

In  As,  and  higher  ancestral  generations,  y|^f  = 
92.97  per  cent  of  the  dam's  ancestors  are  animals 
which  are  also  ancestors  of  the  sire. 

In  Aq,  and  higher  ancestral  generations,  ff§  = 
93.75  per  cent  of  the  dam's  ancestors  are  animals 
which  are  also  ancestors  of  the  sire. 

In  A 10,  and  higher  ancestral  generations,  93.75 
per  cent  of  the  dam's  ancestors  are  animals  which 
are  also  ancestors  of  the  sire. 

In  Aiu  and  higher  ancestral  generations,  93.75 
per  cent  of  the  dam's  ancestors  are  animals  which 
are  also  ancestors  of  the  sire. 

In  A 12,  and  higher  ancestral  generations,  93.75 
per  cent  of  the  dam's  ancestors  are  animals  which 
are  also  ancestors  of  the  sire. 

These  percentages  are  quantities  of  a  good  deal 
of  interest.  They  measure  the  degree  in  which 
King   Melia   Rioter    14th's   sire   and   dam   were 


THE  PROBLEM  OF  INBREEDING       141 


PEDIGREE  TABLE  VU 

Pedigree  for  Four  Ancestral   Generations   of  King  Melia 

Rioter  14th 


X! 

^3 

« 

s 

O 

o 

T-H 

CO 

I> 

6 

< 

OD 

OQ 

p; 

CO 
Oi 
05 
(M 
CO 
(M 

d 

No.  63200     ^ 

Marjorie 

Melia  Ann's 

Son 

No.  56581            Z 
Melia  Ann's  King 

No.  22041  Z 
Melia  Ann's  Son 

No.  100775  9 
Lottie  Melia  Ann 

No.  157263 

Marjorie  Melia 
Ann 

9 

No.  22041  Z 
0  Melia  Ann's  Son 

No.  905883  9 
Mary  Melia  Ann 

No.  181544  9 

Letty  Silver 
Hair 

No.  58169            Z 
King  of  All  Kings 

No.  54896                  Z 
St.  Lambert's  Rioter 
King 

No.  114804  9 
St.  Lambert's  Letty 

t-H 

No.  148456 

Exile's  Silver 
Hair 

9 

No.  32559  Z 
Exile  of  St.  Anne's 

O 

1— 1 

No.  60449  9 
Silver  Hair  4tli 

< 
t— 1 

O 

No.  73104     Z 

0King  Melia 
Rioter 

No.  63200            Z 

X  Marjorie  Melia 
Ann's  Son 

No.  56581  Z 
X  Melia  Ann's  King 

No.  157263  9 
X  Marjorie  Melia  Ann 

No.  181544 

X  Letty  Silver 
Hair 

9 

No.  58169  Z 
X  King  of  All  Kings 

No.  148456                9 
X  Exile's  Silver  Hair 

No.  219360  9 

Dula 

Riotress 

Maid 

No.  62098 

King  Rioter's 
Lad 

Z 

No.  54896                  Z 
0  St.  Lambert's 
Rioter  King 

No.  142296  9 
King's  Riotress  Nora 

o 

No.  218796          9 

St.  Lambert's 
Dula  Riotress 

No.  57778  Z 
St.  Lambert's  Boy 

CO 
o 

I— 1 

d 
12; 

No.  174761                9 
Rioter   Lad's    First 
Daughter 

142    MODES  OF  RESEARCH  IN   GENETICS 

related  to  each  other.     Community  of  ancestry 
is  the  basis  of  kinship. 

Percentages  derived  in  the  way  shown  above, 
from  cross  pedigree  elimination  tables,  I  have 
called  coefficients  of  relationship,  and  designated 
by  the  letter  K,  with  appropriate  sub-numbers 
referring  to  the  generation.  These  relationship 
coefficients  are,  with  some  limitations,  independent 
of  the  inbreeding  coefficients  in  the  values  they 
may  take,  though  the  two  will  usually  be  corre- 
lated to  some  degree.  It  is,  however,  possible 
to  have  a  high  value  of  Z  with  K  =  0. 

The  most  important  feature  of  the  relationship 
coefficients  is  found  in  their  genetic  implications. 
This  can  be  indicated  best  by  an  illustration. 
Let  us  consider  the  case  of  the  maximum  possible 
degree  of  inbreeding  with  K  =  0.  This  will  be 
found  when  the  sire  and  the  dam  are  each  inbred 
to  the  highest  possible  degree  (continued  brother 
X  sister  mating),  but  are  in  no  way  related  to  each 
other.  Such  a  case  would  be  afforded  if  a  Jersey 
bull,  the  product  of  continued  brother  X  sister 
mating,  was  bred  to  a  Holstein  cow,  which 
was  also  the  product  of  a  continued  brother 
X  sister  breeding.  Clearly  K  would  be  0,  since 
no  animal  on  one  half  of  the  pedigree  could  ever 
appear  on  the  other.  The  values  of  the  successive 
coefficients  of  inbreeding  (Z's)  in  such  a  case 
are  shown  in  Table  9,  where  they  are  com- 
pared with  the  coefficients  of  inbreeding  in  com- 


THE  PROBLEM  OF  INBREEDING       143 


TABLE  9 

Comparing  the  Maximum  Possible  Values  of  the  Co- 
efficients OF  Inbreeding  (Z)  when  the  Coefficient 
OF  Relationship  K  Equals  (a)  Zero  and  (6)  100 


Generation 

Maximum  Possible  Value 
of  z  when  k  =  0 

Maximum  Possible  Value 
OP  Z  WHEN  K  =  100 

A, 

0 

0 

A, 

0 

50.00 

As 

50.00 

75.00 

A, 

75.00 

87.50 

A, 

87.50 

93.75 

Ae 

93.75 

96.88 

Ai 

96.88 

98.44 

As 

98.44 

99.22 

A, 

99.22 

99.61 

AlQ 

99.61 

99.80 

plete  continued  brother  X  sister  mating,  where 
K  =  100.1 

From  this  it  appears  that  an  individual  may  be 
inbred  in  10  generations  to  within  two  tenths  of 
one  per  cent  as  intensely,  measured  by  the  co- 
efficients of  inbreeding,  if  his  sire  and  dam  are  in 
no  way  related,  as  he  would  be  if  his  sire  and  dam 
were  brother  and  sister.  But  clearly  the  germinal 
constitution  of  the  individual  produced  would  be 
quite  different  in  the  two  calves.     This  point  is 


*  Since,  of  course,  all  of  a  sister's  ancestors  are  identical  with  her 
brother's. 


144    MODES  OF  RESEARCH  IN   GENETICS 

so  evident  as  to  need  no  elaboration.  It  has  been 
brought  out  by  East  and  Hayes.^ 

The  values  of  the  K's  for  a  particular  pedigree 
evidently  furnish  a  rough  index  of  the  probability 
that  the  two  germ  plasms  which  unite  to  form  an 
individual  are  alike  in  their  constitution.  This 
will  follow  because  of  the  fact  that  the  probability 
of  likeness  of  germinal  constitution  in  two  indi- 
viduals must  tend  to  increase  as  the  number  of 
ancestors  common  to  the  two  increases.  Just 
what  is  the  law  of  this  increase  in  probability  is 
a  problem  in  Mendelian  mathematics  which  has 
not  yet  been  worked  out.  The  general  fact, 
however,  seems  quite  sure. 

From  the  above  discussion  it  seems  plain  that  in 
reaching  a  numerical  measure  of  the  degree  of 
inbreeding  it  is  not  sufficient  to  consider  coefficients 
of  inbreeding  alone.  The  coefficients  of  relation- 
ship must  also  be  taken  into  account. 

It  is  suggested  that  the  two  constants  be  written 
together  for  each  generation,  the  coefficient  of 
inbreeding  being  followed  by  the  coefficient  of 
relationship  in  brackets. 

Thus  we  have 

Inbreeding  and  Relationship  Coefficients  of 
King  Melia  Rioter  14th 

Zo   (K,)  =  0  (0) 

Zi   (^2  )  =  25  (0) 

1  U.  S.  Dept.  Agr.  Bur.  Plant  Industry,  Bui.  243,  1912. 


THE  PROBLEM  OF  INBREEDING       145 

Z2  {Kz  )  =  25.00  (50.00) 
Z3  (X4  )  =  37.50  (62.50) 
Z4  {K5  )  =  50.00  (75.00) 
Z5  {K^  )  =  71.88  (87.50) 
Ze  {K^  )  =  81.25  (92.19) 
Z^  {Ks  )  =  90.63  (92.97) 
Zs  (i^9  )  =  92.77  (93.75) 
Z9  (Xio)  =  93.65  (93.75) 
Zio  (Zii)  =  93.85  (93.75) 
Zii  (ii:i2)  =  93.85  (93.75) 

The  physical  meaning  of  these  expressions  is 
simple  and  straightforward.  Z4  (K5)  tells  that 
in  the  5th  ancestral  generation  of  King  Melia 
Rioter  14th  he  had  only  one  half  as  many  different 
ancestors  as  was  possible  for  that  generation,  and 
of  his  ancestors  three  fourths  were  common  to 
his  sire  and  his  dam.  However  one  looks  at  the 
matter  there  can  be  no  denial  that  King  Melia 
Rioter  14th  is  a  closely  inbred  animal. 

III.   Genetic  Bearing 

Up  to  this  point  the  discussion  of  inbreeding  has 
confined  itself  entirely  to  the  logical  aspects  of 
inbreeding,  considered  as  a  mode  of  mating  indi- 
viduals with  relation  to  their  kinship.  Nothing  has 
been  said,  either  about  the  relation,  if  any,  of 
inbreeding  and  relationship  coefficients  to  the 
zygotic  or  gametic  constitution  (in  the  Mendelian 
sense)  of  the  individual,  or  about  the  physiological 


146    MODES  OF  RESEARCH  IN  GENETICS 

effects  of  inbreeding  upon  the  progeny.  This 
restriction  has  been  dehberate.  The  primary  pur- 
pose of  what  has  preceded  is  to  make  some  con- 
tribution to  the  methodology  of  the  study  of  the 
important  problem  of  inbreeding.  It  has  seemed 
desirable  to  emphasize  the  fact  that  in  the  investi- 
gation of  the  problem  of  inbreeding  in  general 
there  are  three  elements,  which  from  the  stand- 
point of  the  logic  of  the  case,  are  totally  distinct 
and  separate.     These  are  : 

1.  The  logical  and  mathematical  characteristics 
of  a  system  of  mating  of  organisms  such  that  the 
individual  has  fewer  different  ancestors  than  it 
would  have  had  under  the  operation  of  any  other 
system  of  mating.  Having  proper  regard  for  the 
meaning  of  words,  such  a  system  of  mating,  and 
that  alone,  can  logically  be  called  inbreeding. 

2.  The  necessary  consequences  in  respect  of  the 
Mendelian  constitution  of  the  individual  which 
must  follow  the  continued  operation  of  systems  of 
mating  which  are  inbreeding. 

3.  The  physiological  effect  on  the  individual 
consequent  upon  its  having  been  produced  through 
the  operation  of  a  system  of  mating  which  is 
inbreeding. 

The  first  of  these  three  phases  of  the  problem 
is  the  one  attacked  in  the  preceding  sections  of 
this  paper.  In  these  the  attempt  has  been  made 
to  show  in  the  clearest  way  of  which  the  writer  is 
capable  that  inbreeding  is  a  mode  or  system  of 


THE  PROBLEM  OF  INBREEDING       147 

mating  organisms,  and  is,  properly  speaking, 
nothing  else.  Furthermore,  precise  methods  of 
measuring,  and  hence  of  comparing,  systems  of 
mating  which  are  inbreeding  have  been  sug- 
gested in  these  preceding  sections  of  the  paper. 

The  other  two  phases  or  elements  of  the  general 
problem  are  logically  consequences  or  effects  of  the 
first.  The  second  phase  demands  for  its  solution 
mathematical  analysis,  falling  in  the  field  of 
probability,  with,  of  course,  the  limitations  implied 
by  general  Mendelian  principles.  The  third  phase 
demands  experimental  investigation. 

I  have  been  at  considerable  pains  to  endeavor 
to  make  entirely  clear  and  sharply  defined  the 
logical  elements  of  the  problem  of  inbreeding  for 
the  reason  that  the  distinctions  between  them  seem 
not  always  to  have  been  kept  in  mind. 

The  investigation  of  the  second  phase  of  the 
problem  has  barely  been  begun.  It  has  been 
shown  by  East  and  Hayes  ^  and  Jennings  ^  that 
the  proportion  of  homozygotes  increases  steadily 
with  continued  self-fertilization,  which  represents 
the  absolutely  closest  possible  form  of  inbreeding. 
Jennings    summarizes   his    mathematical   results 


1  East,  E.  M.,  and  Hayes,  H.  K.  "Heterozygosis  in  Evolution 
and  in  Plant  Breeding."  U.  S.  Dept.  Agr.  Bur.  Plant  Ind.  Bulletin 
No.  243,  pp.  1-58,  1912. 

2  Jennings,  H.  S.  "Production  of  Pure  Homozygotic  Organisms 
from  Heterozygotes  by  Self-Fertilization."  Amer.  Nat.,  Vol.  XLVI, 
pp.  487-491,  1912. 


148    MODES  OF  RESEARCH  IN  GENETICS 

in  very  convenient  form  as  follows   {loc.  cit.,  p. 
490): 

"Let  X  =  the  proportional  number  of  organisms 
that  are  pure  homozygotes  (with  re- 
spect to  all  the  characters  considered) , 
y  —  proportion     that     are    heterozygotic 
with   respect  to   all    the  characters 
considered, 
s  =  the  proportion  that  are  mixed, 
V  =  the  proportion  that  have  any  heterozy- 
gotic characters. 

Then,    if    n  =  the  number    of    successive  self- 
fertilizations 
and  m  =  the  number  of  pairs  of  characters, 

y  =  (i)"",  (2) 

z  =  l-{x+y),  (3) 


m 


V  =  1  —  X  =  ^ ^—.       (4) 

With  continued  brother  X  sister  mating  the 
present  writer  ^  has  shown  that  the  proportion  of 
homozygotes  also  increases,  in  the  manner  shown 
in  the  following  table. 

1  Pearl,  R.  "On  the  Results  of  Inbreeding  a  Mendelian  Popu- 
lation :  A  Correction  and  Extension  of  Previous  Conclusions."  Amer. 
Nat,  Vol.  XLVIII,  pp.  57-62,  1914. 

Since  this  was  written  a  paper  by  Fish  announcing  an  independent 
working  out  of  the  same  point  has  appeared  (Amer.  Nat.,  1915). 


THE  PROBLEM  OF  INBREEDING       149 

Starting,  by  hypothesis,  with  all  individuals  of 
the  population  heterozygous,  there  will  be 


After  the  Indicated  Numbers  op 
Generations  of  Continued 
Brother  X  Sister  Mating, 

The  Following  Percentage  of 
Homozygotes. 

1 

50.00 

2 

50.00 

3 

62.50 

4 

68.75 

5 

75.0 

6 

79.69 

7 

83.59 

8 

86.72 

9 

89.26 

etc. 

These  results  may  be  put  in  the  form  of  a  general 
formula,  by  means  of  which  the  constitution  of 
any  generation  may  be  written  down  from  a 
knowledge  of  the  preceding  generation;  that  is, 
from  a  knowledge  of  the  n  —  1th  generation  the 
nth  generation  may  be  at  once  written  down. 

This  general  formula  may  be  developed  as  follows. 
A  single  character  pair  will  be  considered,  A  denot- 
ing the  dominant  character  and  a  the  recessive. 
Equal  fertility  for  all  matings  is  assumed,  the  num- 
ber of  individuals  per  family  being  taken  as  2  s,  of 
which  s  are  males  and  s  are  females.  One  family 
will  then  make  s  matings  and  produce  s  families 
in  the  next  generation.  Each  mating  is,  by  hy- 
pothesis, of  a  brother  with  his  sister. 

Starting  as  before  with  a  pair  from  a  population 
in  which  all  individuals  are  of  constitution  ^a,  there 


150    MODES  OF  RESEARCH  IN  GENETICS 

will  be  in  the  next  generation  one  family  of  the 
A  A  -\-  Aa  -\-  aA  +  aa  type.  In  all  succeeding 
generations  there  will  be  six  types  of  families, 
viz. : 

(1)  AA  families. 

(2)  AA  +  Aa  families. 

(3)  Aa  families. 

(4)  A  A  +  2  Aa  -{-  aa  families. 

(5)  Aa  +  aa  families. 

(6)  aa  families. 

The  proportionate  number  of  each  of  these 
types  of  families  will  change  in  successive  genera- 
tions according  to  the  following  system : 

Let  On-i  denote  the  number  of  A  A  families  in  the 
71  —  1th  generation,  and 

Pn-i  denote  the  number  of  A  A  +  Aa  families 
in  the  n  —  1th  generation,  and 

g„_i  denote  the  number  of  ^a  families  in  the 
n  —  1th  generation,  and 

Tn-i  denote  the  number  of  A  A  -j-  2  Aa  -\-  aa 
families  in  the  n  —  1th  generation,  and 

Un-i  denote  the  number  of  ^ a  +  aa  families, 
and 

Vn-i  denote  the  number  of  aa  families. 

It  will  be  possible  to  write  down  u  and  v  in  any 
case  without  calculation  because  of  the  symmetri- 
cal  relations   of   a  Mendelian  population,   since 


THE  PROBLEM  OF  INBREEDING      151 

always  under  normal  conditions  such  as  are  as- 
sumed in  the  general  treatment,  we  have 

Un-l    =    Pn-U 
Vn-1     =    On-U 

t/71  t-^n* 

It  is  necessary,  therefore,  to  consider  only  the 
coeflBcients  for  the  first  four  types  of  family.  In 
the  nth.  generation  the  constitution  of  the  popula- 
tion in  respect  of  families  (not  individuals)  will 
be  as  follows : 

Families  in  the  nth  generation 

=  s{On-i  +  i  Pn-i  +  tV  ^n-i)  AA  families 
+  5  (J  pn-i  +  i  Tn-i)  AA  +  Aa  families 
+  s  (I  Tn-i)  Aa  families 

+   5    (i  Pn-l    +   Qn-l    +   i  Tn-l)   AA 

•^  ^  Aa  -\-  aa  families 
■^  s  {uy^  Aa  -\-  aa  families 
•\-  s  {Vr)  aa  families. 

Or,  taking  coeflScients  alone,  we  have 

On    =    On-l    +  J  Pn-l    +    iV  ^n-1, 
Pn    =    h   Pn-l    +   i  Tn-U 

r„    =    i   Pn-l    +   Qn-l    +   i  Tn-l, 

Let  us  see  how  this  formula  works  out  in  a  con- 


152    MODES  OF  RESEARCH  IN  GENETICS 

Crete  case.     Assume  that  2s  =  32,  or  5  =  16.     Start 
with  a  single  A  A  -{-2  Aa  +  aa  family. 
Then 

On-l    =   0, 

Pn-1    =    0, 

Qn-l    =    0, 

Tn-l    =    1. 

Then  in  the  next  generation  we  shall  have 

16  50  +  i  (0)  +  iV  (1)!   =1  ^^  family 

+  16  SHO)  +  i  (1)S  =  4^AA  +  Aa  families 

+  16  Jl  (l)i   =  2  ^a  families 

+  16  li  (0)  +  0  +  i  (1)S  =^{AA^%Aa-\-aa) 

families 
+  4  (^a  +  aa)  families 
+  1  aa  family. 
This  is  the  fact. 

In  the  next  generation  we  shall  have 

16  {1  +  1  +  iV  (4)i    =  36  AA  families 
+  16  JH4)  +  i  (4)!  =  48  {AA  +  Aa)  families 
+  16  Si  (4)1=  8  ^a  families 
+  16  li  (4)  +  2  +  i  (4,S  =  80  {AA  +2Aa-\-  aa) 

families 
+  48  {Aa  +  aa)  families 
+  36  {aa)  families. 
This  is  the  fact. 

In  the  next  generation  we  shall  have 

16  136  +  i  (48)  +  tV  (80)  S   =  16  X  53  =  848  AA 

families 


THE  PROBLEM  OF  INBREEDING       153 

+  16  Si  (48)  +  i  (80)J   =  16  X  44  =  704  {AA  + 

Aa)  families 
+  16  Jl  (80)1   =  160  ^a  families 
+  16  li  (48)  +  8  +  i  (80)S  =  16  X  52  =  832  {AA 

+  2  Aa  +  ad)  families 
+  704  {Aa  -}-  aa)  families 
+  848  aa  families. 

Succeeding  generations  follow  the  same  law  and 
need  not  be  worked  out  in  detail. 

So  far  the  discussion  has  confined  itself  to 
families,  as  this  must  be  the  basic  unit  in  the 
theory  of  any  form  of  inbreeding.  Turning  to 
individuals,  we  have  the  following  simple  relations 
to  pass  to  individuals : 

In  the  nth  generation  the  number  of 

A  A    (or    aa)    individuals  =25  (o„)  +  5  {pn)   + 

Aa   (or   aA)    individuals  =25    {qn)  +  s  (ip„)  4- 

2  S  [Tji)' 

The  first  of  the  above  expressions  multiplied 
by  2  gives  the  total  heterozygotes. 

The  results  under  certain  conditions  of  brother 
X  sister  and  cousin  mating  have  been  discussed  by 
Jacobs. 1 

Jennings  ^  in  a  very  interesting  and  valuable 

1  Jacobs,  S.  M.  "Inbreeding  in  a  Stable  Simple  Mendelian 
Population  with  Special  Reference  to  Cousin  Marriage.  Proc.  Roy. 
Soc,  Vol.  84,  B,  pp.  23-41,  1911. 

2  Jennings,  H.  S.  "Formulse  for  the  Results  of  Inbreeding." 
Amer.  Nat,  Vol.  XLIII,  pp.  693-696,  1914. 


154     MODES  OF  RESEARCH  IN  GENETICS 

paper  has  given  a  general  formula  for  the  deter- 
mination of  the  percentage  of  homozygotes  (which 
he  calls  the  coefficient  of  homozygosis)  after  n 
generations  of  inbreeding.  His  results  are  as 
follows  : 

"Let  X  =  the  coefficient  of  homozygosis, 

n  =  the  number  of  inbred  generations  (the 
number  of  times  successive  brother 
by  sister  mating  has  occurred), 

/ij  /2j  /sj  etc.,  =  the  successive  terms  of  the  Fibo- 
nacci series  (thus/i  =  0, /2  =  1,  etc.). 

Then  the  formula  for  the  coefficient  of  homozy- 
gosis is : 

2^"i  +/i  .  2"-2  +  f2  .  9,^-K  .  .     etc. 
X  = 

(The  terms  in  the  numerator  are  continued  until 
the  exponent  of  2  becomes  0)." 

It  is  clear  that  for  further  analysis  of  the  problem 
of  inbreeding  there  will  need  to  be  much  more  com- 
prehensive work  done  upon  this  second  phase,  i.e. 
the  theoretical  Mendelian  consequences  of  the 
operation  of  inbreeding.  One  of  the  chief  results 
of  the  present  study,  in  the  writer's  opinion,  is  to 
bring  out  clearly  the  importance  of  a  problem 
which  has  not  yet  been  considered  at  all  in  any  of 
the  discussions  of  the  subject  which  have  hitherto 
appeared.  This  problem  may  be  put  in  the  follow- 
ing way : 

What  is  the  mathematical  probability  that  the 


THE  PROBLEM  OF  INBREEDING       155 

two  individuals,  a  and  h,  which  mated  together 
produce  the  individual  x,  are  of  the  same  zygotic 
constitution  in  respect  of  any  one  or  more  char- 
acters, when  they  have  1,  2,  3,  4,  .  .  .  m  common 
ancestors  in  the  nth  ancestral  generation? 

This  I  believe  to  be  the  crucial  outstanding 
problem  of  Mendelian  mathematics  in  relation  to 
inbreeding.  Its  solution  ought  to  be  in  principle 
simple,  if  somewhat  tedious  in  the  carrying  out. 
As  has  already  been  pointed  out  (p.  145,  supra),  it 
seems  likely  on  a  priori  grounds  that  this  probabil- 
ity will  be  found  always  to  bear  a  definite  relation 
to  the  coefficients  of  relationship.  If  this  be  true, 
it  will  be  of  great  help  practically  in  studying 
inbreeding,  since  it  is  always  a  simple  matter  to 
determine  coefficients  of  relationship. 

Finally,  to  summarize  briefly  this  rather  ex- 
tended discussion  of  the  logical  aspects  of  the 
problem  of  inbreeding,  it  may  be  said  that  in  this 
paper  has  been  presented,  first,  a  general  method 
of  measuring  the  intensity  or  degree  of  the  in- 
breeding practiced  in  any  particular  case.  The 
method  proposed  is  shown  to  be  perfectly  general. 
It  is  based  on  no  assumption  whatever  as  to  the 
nature  of  the  hereditary  process.  On  the  con- 
trary, it  is  founded  on  the  most  completely  logical 
and  comprehensive  definition  of  the  concept  of 
inbreeding  that  it  seems  possible  to  formulate. 
This  is,  in  simplest  form,  that  the  fundamental 
objective  criterion  which  distinguishes  an  inbred 


156    MODES  OF  RESEARCH  IN  GENETICS 

individual  from  one  not  inbred  is  that  the  former 
has  fewer  different  ancestors  than  the  latter.  It 
is  believed  that  the  proposed  coefficients  of  inbreed- 
ing may  be  made  extremely  useful  in  studies  of 
the  problem  of  the  effect  of  inbreeding,  whether 
in  relation  to  its  purely  theoretical  aspects,  or  in 
the  practical  fields  of  stock  breeding  and  eugenics. 

In  the  second  place,  attention  is  called  to  the 
fact  that  inbreeding  of  considerable  degree  may  be 
brought  about  in  the  entire  absence  of  any  kinship 
between  the  two  individuals  bred  together,  and  there 
is  described  a  method  of  separately  measuring  what 
proportion  of  the  observed  inbreeding  in  a  par- 
ticular case  is  due  to  kinship  of  the  parents,  and 
what  to  earlier  ancestral  reduplication.  A  pro- 
posed coefficient  of  relationship  is  described,  and 
its  application  illustrated  by  concrete  cases. 

In  a  final  section  it  is  shown  that  logically  the 
general  problem  of  inbreeding  must  be  considered 
as  composed  of  three  distinct  elements,  viz. : 

1.  Inbreeding  itself  —  a  system  of  mating  with 
definite  mathematical  characteristics. 

2.  The  genetic  consequences  of  inbreeding. 

3.  The  physiological  consequences  of  inbreed- 
ing. A  discussion  of  the  second  of  these  elements, 
the  first  two  sections  of  the  paper  having  been 
devoted  to  a  consideration  of  the  first,  reviewed 
the  meager  work  so  far  done  on  the  theoretical 
side  of  the  problem.  No  attempt  is  made  here  to 
discuss  in  any  way  the  third  element  of  the  problem. 


CHAPTER  V 

GENETICS  AND  BREEDING  i 

One  of  the  primary  purposes  for  which  the 
American  Breeders'  Association  was  founded  was 
to  bring  together  on  a  common  ground  those  who 
were  approaching  the  problem  of  the  improvement 
of  plants  and  animals  by  breeding,  on  the  one 
hand,  from  the  side  of  practical  breeding,  and, 
on  the  other  hand,  from  the  side  of  the  scientific 
study  of  heredity.  One  of  these  groups  stands  as 
the  representative  of  the  art  or  craft  of  breeding, 
and  the  other  as  the  representative  of  the  science 
of  genetics.  That  each  of  these  two  bodies  of 
men  has  something  to  learn  from  the  other  there  is 
no  doubt.  Even  with  the  continued  and  prosper- 
ous existence  of  such  an  association  as  this  it  is 
certain  that  actually  there  is  far  from  being  any- 
thing like  as  extensive  a  mutual  interchange  of 
knowledge  and  opinion  between  science  and  prac- 
tice in  breeding  as  would  appear  from  every  point 
of  view  to  be  desirable. 

1  Address  of  the  retiring  chairman  of  the  Animal  Section  of  the 
American  Breeders'  Association  at  its  Columbia,  S.C.,  meeting  in 
January,  1913.  Originally  printed,  in  slightly  different  form,  in 
Science,  Vol.  XXXVII,  pp.  539-546,  1913. 

157 


158    MODES  OF  RESEARCH  IN  GENETICS 

It  will  have  been  perceived  by  all  who  have  fol- 
lowed my  remarks  so  far  that  they  have  been  com- 
monplace to  the  point  of  utter  banality.  They 
constitute  a  thoroughly  bromidic  introduction  to 
a  conventional  treatment  of  that  time-stained  and 
battle-scarred  old  theme  of  compulsory  oratory, 
the  relation  of  science  and  practice.  Every  one 
can  foresee,  with  a  moment's  reflection,  just  what 
ought  to  come  next,  and  next,  and  on  to  the  end.  At 
the  outstart  should  be  set  forth  the  great  achieve- 
ments of  the  science  of  genetics ;  then  should  be 
sketched  the  tremendous  possibilities  thus  opened 
out  to  the  practical  breeder,  who  in  the  near  future 
will  be  able  to  soar  from  this  scientific  foundation 
to  realms  of  wealth  and  power  in  the  community 
hitherto  possible  only  to  the  predatory  classes; 
nevertheless,  in  a  meek  and  humble  spirit  of  grati- 
tude engendered  by  the  blessings  which  have  been 
poured  at  his  feet,  he  in  turn  contributes  to  the 
great  cause  of  science  by  placing  at  the  disposal 
of  the  geneticist  the  wonderful  stores  of  experience 
he  has  accumulated ;  at  the  end  should  come  an 
impassioned  plea  for  "getting  together"  for  the 
good  of  agriculture,  humanity,  and  sundry  other 
things,  which  should,  if  well  done,  so  titillate  the 
emotions  as  to  send  everybody  home  uplifted,  and, 
in  general,  determined  to  lead  a  better  life. 

I  have  sketched  this  little  picture,  which,  if 
necessarily  impressionistic,  is  essentially  true, 
only  to  bring  into  sharp   relief   the  intellectual 


GENETICS  AND  BREEDING  159 

junction  point,  at  which  we  shall  alight  and  change 
cars.  Just  because  there  has  been  so  much  per- 
fervid  oratory,  loose  thinking,  and  cheap  adver- 
tising of  the  achievements  of  men  and  institutions 
based  on  the  ideal  or  assumed  mutual  interrela- 
tionship of  the  science  of  genetics  and  the  breeders' 
art,  it  seems  worth  while  to  make  a  careful  ob- 
jective analysis  of  the  actually  existing  relations 
between  these  adjoining  fields  of  human  endeavor. 
Such  an  analysis  will  be  attempted  in  what  follows. 
Specifically  the  question  to  which  attention  is  in- 
vited is :  What  essential  and  fundamental  con- 
tributions has  genetics  made  to  the  "practice  of 
the  breeders'  art?  Or,  to  put  the  matter  in 
another  way,  what  particular  things  does  the 
most  highly  successful  practical  animal  breeder 
do  now  which  he  did  not  do,  or  performed 
differently,  before  Mendelism  was  rediscovered 
or  Darwin  wrote  ? 

It  is  generally  agreed  that  during  the  past 
fifteen  years  there  has  been  a  great  advance  in 
our  knowledge  of  the  fundamental  laws  of  hered- 
ity. Indeed,  it  may  fairly  be  said  that  more  has 
been  gained  in  this  regard  within  this  period  than 
in  the  entire  previous  history  of  this  field  of  knowl- 
edge. The  new  method  of  investigating  heredity 
which  was  given  by  Mendel's  work  has  for  the 
first  time  made  a  real  analysis  of  genetic  phenom- 
ena possible.  It  was  a  truly  imposing  array  of 
organisms  and  characters  which  Major  Hurst  was 


160    MODES  OF  RESEARCH  IN   GENETICS 

able  to  list  at  the  meeting  in  commemoration  of 
Mendel  at  Brunn,  as  comprising  those  attributes 
of  organisms  about  the  inheritance  of  which  some- 
thing definite  is  known. 

There  is  a  very  widespread  assumption  that 
coincident  with  this  advance  in  our  knowledge  of 
the  fundamental  laws  of  inheritance  there  has  been 
an  equal  advance  in  the  practical  art  of  breeding. 
This  has  perhaps  resulted  from  the  somewhat  over- 
enthusiastic  prophecies  of  the  early  Mendelian 
workers.  Many  will  remember  the  glittering 
possibilities  set  forth  to  the  practical  breeders  in 
the  early  meetings  of  this  association.  They  were 
told  in  effect  that  at  last  the  key  to  the  genetic 
riddle  had  been  found ;  that  by  the  application  of 
these  simple  Mendelian  laws  existing  races  of 
animals  could  be  brought  up  to  desired  ideals  with 
more  certainty  and  dispatch  than  had  hitherto 
been  possible,  and  that  new  races  could  be  created 
which  would  surpass  in  usefulness,  anything  now 
existing.  There  was,  of  course,  an  element  of 
truth  in  all  this.  But  it  raised  unwarranted  hopes 
in  the  minds  of  many  laymen.  The  apparent 
failure  of  these  prophecies  to  be  realized  has  prob- 
ably done  real  harm  to  the  cause  of  science  in 
the  minds  of  some  practical  men  —  representa- 
tives of  the  class  to  which  in  last  analysis  science 
must  look,  for  its  material  support  —  and  very 
generally  has  led  animal  breeders  to  underrate  the 
real  value  of  Mendelian  investigations. 


GENETICS  AND  BREEDING  161 

It  is  permissible  to  think  that  the  fundamental 
error  involved  was  in  the  assumption  we  are  all 
inclined  to  make  that  any  distinct  advance  in 
science  necessarily  means  an  equally  marked  and 
immediate  advance  in  the  practice  of  the  associ- 
ated art  or  craft.  It  is  extremely  difficult  for  the 
man  of  the  laboratory  or  the  study,  as  he  takes  a 
broad  view  of  the  history  of  the  industrial  arts,  and 
sees  that  great  progress  there  has  rested  upon 
fundamental  scientific  discoveries,  to  realize  that 
the  art  of  breeding  differs  essentially  in  this  re- 
spect from  the  industrial  arts.  The  breeding  of 
animals  by  man  for  more  or  less  definite  purposes 
goes  back  to  prehistoric  times.  Practically  as 
soon  as  primitive  man  began  the  domestication  of 
animals  he  must  perforce  have  begun,  in  greater 
or  less  degree,  to  control  their  breeding.  Having 
started  thus  early,  the  craft  of  breeding  had  at- 
tained a  relatively  high  degree  of  development 
centuries  before  any  attempt  was  made  to  for- 
mulate the  scientific  principles  of  genetics.  As 
an  example  may  be  mentioned  the  breeding  of 
horses  in  England.  It  is  customary  to  think  of 
"stallion  laws,"  aimed  at  the  improvement  of 
the  horses  of  a  state,  as  very  modern  and 
American,  and  an  indication  of  the  influence  of 
the  science  of  breeding  on  the  practical  craft. 
But  three  hundred  and  seventy-odd  years  ago,  in 
the  reign  of  Henry  VIII,  there  was  a  "bill  for  the 
breed  of  horses,"  which  in  preamble  stated  that : 

M 


162    MODES  OF  RESEARCH  IN  GENETICS 

"Forasmuch  as  the  generation  and  breed  of 
good  strong  horses  within  this  realm  extendeth 
not  only  to  a  great  help  and  defence  of  the  same, 
but  also  is  a  great  commodity  and  profit  to  the 
inhabitants  thereof,  which  is  now  much  decayed 
and  diminished  by  reason  that,  in  forests,  chases, 
moors  and  waste  grounds  within  this  realm,  little 
stoned  horses  and  nags  of  small  stature  and  of 
little  value  be  not  only  suffered  to  pasture  there- 
upon, but  also  to  cover  mares  feeding  there,  where- 
of Cometh  in  manner  no  profit  or  commodity." 

In  order  to  prevent  the  multiplication  of  poor 
specimens  section  2  of  this  law  provided  that  no 
uncastrated  stallion  two  years  or  more  old  which 
was  under  15  "handfulls"  high  should  be  allowed 
to  graze  on  common  or  waste  land  in  certain 
counties.  Further,  it  was  provided  in  section  6 
that  all  forests,  chases,  commons,  etc;,  were  to  be 
"driven"  at  a  stated  time  in  the  year  (just  pre- 
ceding Michaelmas  day)  and  all  horses,  mares,  and 
colts  which  were  not  of  good  quality,  or  did  not 
promise  to  become  or  to  produce  serviceable  ani- 
mals, were  to  be  killed. 

The  fact  is  that  the  practice  of  the  art  of  animal 
breeding,  so  far  from  languishing,  for  want  of  in- 
struction from  the  science  of  genetics  is  actually 
immeasurably  in  advance  of  that  science.  The 
geneticist  who  is  disposed  to  think  otherwise  should 
visit  a  great  horse,  or  cattle,  or  even  poultry  show, 
and  then  permit  himself  to  consider  candidly  the 


GENETICS  AND  BREEDING  163 

question  whether  with  all  his  science  he  could  him- 
self breed,  or  tell  any  one  else  how  to  produce, 
finer  specimens  than  he  will  see  there.  Yet  by 
hypothesis  that  is  exactly  what  he  ought  to  be 
able  to  do,  if  genetics  is  to  set  up  as  a  teacher  and 
guide  to  the  best  practical  methods  of  live-stock 
breeding. 

It  is  capable  of  abundant  historical  proof  that 
many  years  ago,  before  the  beginning  of  the  world 
movement  towards  agricultural  education,  experi- 
mentation and  the  grounding  of  a  science  of  agri- 
culture in  general,  there  were  in  existence  indi- 
vidual animals  (even  flocks  and  herds) ,  and  strains 
of  seeds  of  farm  crops  which  were  probably  in- 
trinsically as  fine,  as  productive,  and  generally  as 
excellent  as  any  that  we  know  to-day.  Given  as 
intelligent  care  and  feeding  as  our  prize-winning 
animals  and  plants  now  get,  there  is  every  reason 
to  believe  that  they  would  have  equaled  or  sur- 
passed our  finest  specimens  of  to-day.  Some 
specific  examples  may  be  cited.  Mr.  George  A. 
Scott,!  of  Nashville,  Tenn.,  had  in  1863  "a  com- 
mon scrub  cow"  which  produced  in  one  year 
1447|  gallons  of  milk.  Taking  the  weight  of  one 
quart  of  milk  at  2.15  lbs.  as  sufficiently  close  for 
practical  purposes,  this  gives  a  record  of  12,448.5 
lbs.  of  milk  for  the  year.  This  is  a  respectable 
figure  even  for  present  standards.  Going  back 
half  a  centurv  earlier,  we  have  the  record  of  a 

^  The  Cultivator  and  Country  Gentleman,  Vol.  28,  p.  401,  1866. 


164    MODES  OF  RESEARCH   IN  GENETICS 

Sussex  cow :  ^  "a  cow  not  of  either  of  the  highest 
improved  Enghsh  breeds  —  long  horns  or  short 
horns ;  but  of  the  proper  old  Sussex  breed."  The 
following  record  is  of  her  production  in  five  suc- 
cessive years  beginning  in  1805.  I  have  tran- 
sposed quarts  to  pounds  by  the  use  of  the  factor 
given    above : 


First  year 
Second  year 
Third  year 
Fourth  year 
Fifth  year 


Weeks  in 
Milk 


48 

42| 

48 


Lbs.  of 
Milk 


10,580.2 
8,894.6 

12,366.8 
9,070.9 

11,543.4 


Lbs.  of 
Butter 


540 
450 
675 
466 
594 


Facts  of  the  same  sort  are  at  hand  for  crops. 
Justin  Ely,  Esq.,  of  West  Springfield,  Mass.,  in 
1816,  raised  50  bushels  of  wheat  to  the  acre.  Colo- 
nel James  Valentine,  of  Hopkinton,  raised  128 
bushels  of  "Indian  corn"  to  the  acre.  Payson  Wil- 
liams, Esq.,  of  Fitchburg,  raised  614  bushels  of  pota- 
toes to  the  acre,  and  James  Whitton,  Esq.,  of  Lee, 
raised  85  bushels  of  oats  to  the  acre.  The  average 
yield  of  oats  to-day  is  approximately  36  bushels  to 
the  acre.  The  Maine  Agricultural  Experiment 
Station,  in  its  tests  of  the  best  commercial  varie- 
ties of  oats  procurable  in  this  country  and  Europe, 

^  Massachusetts  Agricultural  Repository  and  Journal,  Vol.  IV, 
No.  4.     Cf.  also  New  England  Farmer,  Vol.  Ill,  p.  305,  1825. 


GENETICS  AND  BREEDING  165 

has,  up  to  the  time  of  writing,  never  been  able  to 
obtain  a  yield  per  acre  of  more  than  76  bushels.^ 

I  have  elsewhere  discussed  records  of  egg  pro- 
duction in  poultry  in  this  connection.  From  1836 
there  is  an  authenic  record  of  crested  Polish  fowls 
producing  an  average  of  175  eggs  each  per  year. 
This  was  long  before  the  trap  nest  had  been  dis- 
covered. 

Too  much  stress,  of  course,  should  not  be  laid 
on  such  examples  as  these.  They  do  not  indicate 
that  there  has  been  no  advance  made  by  the 
breeder  in  the  qualities  of  domesticated  animals 
and  plants  during  the  last  century.  The  average 
quality  of  live  stock  and  of  crop  plants  is  con- 
stantly improving,  not  only  as  a  result  of  breeding 
but  also  because  of  better  and  more  widely  dis- 
seminated knowledge  of  how  to  provide  the  food 
and  environmental  conditions  best  suited  to 
bring  to  full  expression  the  potential  hereditary 
capabilities  ^  of  the  individual.  I  think  that  such 
records,  however,  do  fairly  indicate  that  in  the 
practice  of  the  art  of  breeding  there  has  been  no 
such  marked  fundamental  advance  in  recent  years 
as  there  has  been  in  the  science  of  genetics.  By 
empirical    methods    man   has   been   steadily   im- 


1  In  the  season  of  1914  this  was  exceeded. 

2  Consider  in  this  connection  the  practices  of  the  real  expert  in 
making  world's  records  for  milk  and  butter  fat  production  in  the 
seven-  and  thirty-day  advanced  registry  tests  of  the  Holstein-Friesian 
breed. 


166     MODES  OF  RESEARCH   IN   GENETICS 

proving  the  quality  of  live  stock  for  centuries  past, 
and  long  ago  a  relatively  high  level  was  reached  by 
the  most  skillful  breeders. 

Furthermore,  in  this  same  connection,  the  fact 
must  not  be  lost  sight  of,  that  in  the  practice  of 
the  breeder's  art  many  of  the  most  brilliant  suc- 
cesses are  purely  accidental,  in  the  sense  that  the 
superior  individual  often  appears  quite  without 
relation  to  the  breeder's  conscious  or  planned 
efforts.  A  few  examples  will  suffice  to  illustrate 
this  point.  Mr.  Oscar  Tretsven  of  the  Montana 
Agricultural  College,  has  reported  recently  ^  the 
particulars  in  regard  to  the  performance  of  a  grade 
Jersey  cow  purchased  in  Minnesota.  No  particu- 
lars of  its  breeding  were  given.  It  was  just  a 
"grade,"  that,  like  Topsy,  "growed."^  However, 
her  record  for  a  year  was  16,286.1  lbs.  of  milk, 
844.8  lbs.  of  fat  (=  1056  lbs.  of  80  %  butter).  In 
a  seven-day  test  she  produced  450.2  lbs.  of  milk 
and  21.245  lbs.  fat.  Her  yearly  record,  at  the 
time  it  was  made,  put  her  fifth  in  the  list  of  high- 
est producing  (world's  record)  cows  of  the  Jersey 

»  *' Hoard's  Dairyman,  Vol.  XLIII,  p.  695,  May  31,  1912. 

2  In  a  letter  of  July  14,  1914,  Professor  R.  F.  Miller  very  kindly 
gives  me  the  following  information  about  this  cow :  "  I  may  say  that 
we  do  not  know  anything  about  her  breeding.  She  was  simply 
bought  in  Minnesota  from  a  Polish  farmer  with  a  lot  of  other  grade 
milch  cows.  The  man  we  bought  her  of  was  not  making  dairying  a 
specialty  and  had  probably  not  bred  his  stock  very  strictly  in  that 
direction.  We  consider  her  to  be  a  grade  Jersey,  although  she  shows 
some  Guernsey  blood  and  a  Shorthorn  frame." 


GENETICS  AND  BREEDING  167 

breed.  The  only  four  records  then  exceeding 
that  of  this  grade  cow  were  those  of  the  famous 
Jersey  cows,  Jacoba  Irene,  Sophie  19th  of  Hood 
Farm,  Olga's  4th  Pride,  and  Adelaide  of  Beech- 
land. 

Another  similar  example  is  found  in  a  recent 
report  of  the  performance  of  a  scrub  cow  in  Wash- 
ington, D.C.i  Since  this  report  is  very  brief,  it 
may  be  quoted  in  full. 

"An  old  black  scrub  cow  No.  131  in  a  local 
government  herd  was  last  fresh  Oct.  6,  1909,  and 
has  since  been  sterile,  due  to  old  age  (probably  15 
to  20  years  old).  From  this  date  to  Aug.  1,  1913, 
she  has  made  33,066  lbs.  of  milk." 

This  is  a  remarkable  record,  and  it  is  quite  clear 
that  neither  the  science  of  the  geneticist  nor  the 
art  of  the  breeder  had  anything  to  do  with  the  pro- 
ducing of  this  old  black  scrub. 

Purely  empirical  methods  are  wasteful  and 
slow  in  operation,  but  they  may  attain  excellent 
results.  When  they  are  successful  it  is  obviously 
because  at  just  that  point  the  practice  was,  by 
chance,  in  exact  conformity  with  the  underlying 
principle  or  law  concerned.  More  generally  it 
may  be  said  that  all  progressive  success  of  em- 
pirical methods  depends  on  a  gradual  elimination 
of  those  operations  or  practices  which  do  not  accord 
with  basic  natural  laws.  In  the  consideration  of 
the  science  and  practice  of  breeding  this  has  some- 

1  Hoard's  Dairyman,  Vol.  XLVI,  p.  175,  Sept.  \i,  1913. 


168    MODES  OF  RESEARCH  IN  GENETICS 

times  been  forgotten.  It  is  difficult  to  remember 
always  that  a  law  of  nature  may  be  presumed  to 
have  been  in  operation  before  its  discovery.  If 
Mendel's  law  represents  a  real  and  fundamental 
law  of  nature,  as  certainly  appears  to  be  the  case  in 
the  light  of  present  evidence,  it  is  quite  certain 
that  it  did  not  begin  operation  in  a.d.  1900. 
Whatever  of  success  has  been  attained  during 
centuries  past  in  the  breeding  of  improved  strains 
of  animals  and  plants  must  have  been  attained  by 
methods  and  practices  which  were  not  violently 
in  discord  with  Mendelian  principles.  A  nomad 
Arab  may  never  have  heard  of  the  principle  of 
segregation,  but  none  the  less  he  had  to  reckon 
with  the  phenomenon  in  breeding  his  horses. 

Looking  at  the  matter  in  this  way,  the  reason 
is  clear  why  the  rediscovery  of  Mendel's  work  and 
the  brilliant  genetic  researches  which  have  fol- 
lowed did  not  and  could  not  have  had  any  pro- 
found revolutionary  effect  on  the  practice  of  the 
animal  breeders'  art.  By  years  —  even  centuries 
—  of  *' trial  and  error  "  methods,  breeding  practice 
has  been  brought  into  rather  close  conformity 
with  the  basic  laws  of  heredity.  The  discovery 
of  some  of  these  laws  by  the  geneticist  could  not 
radically  change  the  breeder's  way  of  attaining 
results. 

What  then  has  the  rapidly  developing  science  of 
genetics  done  for  the  breeder  and  what  can  it  do  ? 
Still  looking  at  the  matter  from  the  standpoint  of 


GENETICS  AND   BREEDING  169 

the  practical  animal  breeder,  it  must  be  agreed, 
I  think,  that  the  chief  contribution  of  recent  dis- 
coveries in  the  field  of  inheritance  is  that  they  have 
brought  to  light  and  fairly  established  certain  gen- 
eral principles  which  enable  him  in  greatly  in- 
creased measure  to  understand  and  interpret  his 
methods  and  his  results.^  This  may  seem  too 
mild  a  statement  of  the  practical  value  of  genetic 
science  to  the  animal  breeder.  It  undeniably  does 
lack  the  grandeur  of  the  vision  sometimes  opened 
out  by  the  extension  lecturer  in  his  zeal  to  inspire 
the  farmers  to  better  things,  and  at  the  same  time 
pave  the  way  to  increased  appropriations  for  his 
institution.  But  to  help  one  to  understand  and 
to  interpret  is,  after  all,  no  mean  achievement.  It 
signifies  that,  with  much  economy  of  effort,  the 
successful  breeder  may  dispense  with  the  merely 
trivial  and  unessential  in  his  empirical  methods, 
and  more  directly  and  uniformly  attain  the  same 
or  a  greater  measure  of  success  than  before.  To 
his  less  successful  brother  and  the  beginner,  it 
means  a  surer  and  more  rapid  guide  than  the  old 
tradition  based  on  empiricism.     It  is  certain  that 

^  This  is  of  course  to  be  understood  as  a  general  statement.  There 
are  now  a  few  specific  instances,  and  in  time  there  will  be  more,  where 
the  geneticist  has  been  able  to  show  the  breeder  precisely  how  to 
attain  a  particular  result  in  breeding  commercially  for  a  particular 
quality,  which  result  he  had  only  hitherto  been  able  to  obtain  by 
chance.  In  no  such  case,  however,  so  far  as  I  am  aware,  has  the 
new  method  been  so  essentially  different  from  former  practice  as  to 
be  fairly  regarded  as  "revolutionary." 


170    MODES  OF  RESEARCH   IN   GENETICS 

the  young  man  starting  out  to-day  to  be  a  breeder 
of  fine  cattle,  of  fine  horses,  of  fine  chickens,  is 
likely  to  attain  his  goal  somewhat  sooner  if  he 
thoroughly  understands  the  meaning  of  those  laws 
of  inheritance  associated  with  the  name  of  Mendel. 

The  most  important  general  principles  which 
the  scientific  study  of  genetics  has  firmly  grounded 
are,  it  seems  to  me,  these : 

(a)  That  the  fundamental  basis  of  all  inheritance 
is  to  be  found  in  the  germinal  constitution  of  the 
individual  rather  than  in  the  body  or  soma.  Those 
qualities  alone  are  inherited,  which  are  innate  in 
the  germ  cells,  the  ova  and  the  spermatozoa.  Here 
only  can  the  breeder  find  the  means  with  which  to 
accomplish  his  ends.  However  interesting  theoret- 
ically may  be  those  rare  and  still  doubtful  cases 
in  which  extraordinary  influences  acting  upon  the 
body  under  the  controlled  and  special  conditions 
of  the  laboratory  may  perhaps  influence  the  germ 
cells  through  the  soma,  they  have  no  bearing  on 
the  practical  conduct  of  the  breeders'  craft.  Ge- 
netics has  demonstrated  that  he  may  cast  aside, 
for  once  and  all,  that  mass  of  tradition  and  super- 
stition which  assumed  that  influences  specifically 
affecting  the  body  will  specifically  modify  subse- 
quent generations.  Has  not  genetics  done  breed- 
ing a  service  of  great  value  in  freeing  it  of  the 
sinister  influence  of  "telegony,"  "saturation," 
"maternal  impressions  "  and  similar  sorts  of  non- 
sense ? 


GENETICS   AND   BREEDING  171 

(6)  That  specific  characters  or  groups  of  char- 
acters, in  the  great  majority  of  cases  and  perhaps 
all,  are  inherited  as  discrete  and  definite  units. 
If  one  mates  a  pea-combed  fowl  with  a  single- 
combed  fowl,  all  the  offspring  will  have  pea-combs. 
This  result  occurs  whether  the  pea-combed  parent 
is  a  Game  or  a  Brahma ;  whether  it  is  a  male  or  a 
female ;  w^hether  it  is  a  strong,  vigorous  individ- 
ual, or  the  sickliest,  weakest  scrub  in  the  flock. 
In  other  words,  the  Idnd  of  a  bird  it  is  whose  germ 
cells  carry  the  potentiality  to  make  pea-combs 
develop  in  the  offspring,  so  far  as  we  now  know, 
has  nothing  to  do  with  the  specific  result  {i.e.,  the 
production  of  a  'pea-comhy  rather  than  a  single,  a 
rose,  or  any  other  kind).  Comb  form  is  inherited 
as  a  discrete  unit  largely,  if  not  completely, 
uninfluenced  by  the  individual's  other  attributes. 
This  discovery  that  many  characters  are  inherited 
as  separate  units  —  and  no  principle  of  genetics 
is  more  firmly  grounded  than  this  —  gives  the 
breeder  a  totally  new  concept  of  the  meaning 
of  "purity"  of  blood  in  breeding.  We  see  now 
that  properly  {i.e.,  biologically)  one  can  only 
speak  of  an  animal  as  being  "pure-bred"  when 
he  specifies  the  particular  character  to  which  he 
refers.  A  chick  may  be  the  veriest  mongrel  in 
all  other  respects  and  yet  carry  in  the  germ  cells 
only  that  potentiality  in  respect  of  comb  form 
which  leads  to  the  development  of  a  pea-comb. 
Then  however  much  of  a  mongrel  it  may  be  in 


172    MODES  OF  RESEARCH  IN   GENETICS 

respect  of  all  other  characters,  it  is  *'pure"  and 
"pure-bred"  so  far  as  concerns  comb.  Is  it  not 
a  contribution  of  moment  to  the  breeder  to  have 
demonstrated  that  in  his  breeding  operations  he 
may  safely  and  surely  deal  with  individual  char- 
acters, and  groups  of  correlated  characters  as  units  ? 

(c)  That  in  a  very  great  range  of  cases,  per- 
haps in  all  —  the  number  of  known  cases  daily 
grows  larger  —  the  Mendelian  law  of  segregation 
and  recombination  of  characters  operates.  In  the 
formation  of  the  germ  cells  of  an  individual  there 
is  a  sorting  out  or  segregation  of  the  hereditary 
characteristics  contributed  by  the  father  and  the 
mother  and  a  readjustment  of  these  into  all  of  the 
combinations,  both  old  and  new,  which  are  mathe- 
matically possible.  What  may  be  the  precise  cel- 
lular mechanism  or  basis  of  this  wonderful  process 
is  not  altogether  certain,  but  the  phenomenon  it- 
self is  as  certain  as  the  phenomenon  of  gravitation. 
It  operates  as  well  in  regard  to  the  minutest  heri- 
table differences  in  the  pedigreed  specimens  of  the 
same  sub-breed  as  in  the  wide  differences  of  true 
hybridization.  Properly  understood,  it  enables 
the  breeder  to  interpret  and  weigh  the  results  of 
his  breeding  operations,  and  so  intelligently  to 
plan  the  next  steps  with  a  certainty  and  precision 
hitherto  unattainable.  Is  not  this  a  real  contri- 
bution of  science  to  practice  ? 

(d)  That  the  germinal  bases  of  heritable  unit 
characters  can  be  changed  or  altered  in  any  respect. 


GENETICS  AND   BREEDING  173 

only  with  the  greatest  difficulty,  if  at  all.  It  is,  I 
believe,  fair  to  say  that  there  is  at  present  no 
critical,  unchallenged  evidence  that  any  alteration 
can  be  produced.  This  matter  has  recently  been 
discussed  in  a  most  able  manner  by  East.^  The 
weight  of  evidence  at  present  indicates  that  selec- 
tion does  not  act  in  the  manner  it  was  long  sup- 
posed to,  in  accordance  with  Darwin's  interpreta- 
tion. It  appears  that  selection,  however  stringent 
or  long  continued,  is  powerless  to  alter  in  any  way 
the  original  potentialities  of  the  germinal  basis 
of  a  unit  character.  Selection  appears  to  be  es- 
sentially a  process  of  sorting  out  from  a  mixture  of 
heritable  variations  what  is  already  there,  and  not 
a  germinally  creative  or  germinally  additive  pro- 
cess. 

So  far  this  discussion  has  been  approached  from 
the  standpoint  solely  of  animal  breeding.  It  is 
perhaps  allowable,  even  before  this  animal  section, 
to  digress  for  a  little  and  discuss  plant  breeding. 
The  ultimate  objective  point  of  the  animal  breeder 
is  the  same  as  that  of  the  plant  breeder ;  namely, 
the  greatest  possible  improvement  of  animals  and 
plants  and  their  adaptation  to  the  needs  of  man. 
The  practical  method  of  working  towards  this 
goal  is,  however,  somewhat  different  in  the  two 
fields.  The  animal  breeder  almost  exclusively 
works  towards  the  amelioration  of  existing  fixed 
and  "pure"  breeds.     Especially  among  the  larger 

^  American  Naturalist,  1912. 


174    MODES  OF  RESEARCH  IN  GENETICS 

domestic  animals  such  a  thing  as  a  new  breed  is 
brought  forward  by  the  breeder  only  on  very  rare 
occasions.  Almost  all  of  our  existing  breeds  of 
horses,  cattle,  sheep,  and  swine  have  long  histories 
as  "pure  breeds,"  and  no  new  ones  are  being  added 
now.  With  smaller  animals  such  as  poultry  the 
case  is  of  course  somewhat  different.  There  we 
have  no  registered  pedigrees  and,  with  some  dif- 
ficulty, new  breeds  may  be  launched. 

The  plant  breeder,  on  the  other  hand,  makes 
nearly  all  of  his  improvements  by  the  production 
of  new  varieties.  This  he  does  either  by  hybridi- 
zation, actually  building  up  a  new  type,  or  by 
isolation  of  superior  pure-breeding  forms  from 
already  existing  mixtures.  He  is  not  hampered 
by  a  body  of  tradition  that  only  the  "pure-bred  " 
is  of  any  particular  value.  Almost  if  not  quite 
every  one  of  the  most  valuable  strains  of  agricul- 
tural plants  to-day  carries  the  "bar  sinister."  To 
the  animal  breeder  they  would  be  "grades"  or 
"crosses"  however  gametically  pure,  and  only  with 
the  greatest  difficulty  would  ever  have  gained  a 
chance  to  show  their  worth. 

No  one  would  deny  that  the  systems  of  registry 
for  live  stock  and  the  exploitation  of  the  "pure- 
bred" have  been  of  great  value  in  the  develop- 
ment of  the  animal  industry  of  the  world.  They 
certainly  have;  and  every  day  the  economic 
importance  of  the  system  becomes  greater,  for 
obvious  reasons.     All  systems  of  pedigree  registra- 


GENETICS  AND  BREEDING  175 

tion  operate  economically  precisely  like  a  monop- 
oly. As  such  a  plan  of  developing  the  live-stock 
industry  of  a  country  grows,  the  more  difficult 
does  it  become  for  a  new  creation  of  the  breeder  to 
get  a  foothold.  If  it  is  new,  it  is  by  definition  not 
"pure-bred,"  because  if  it  were  "pure-bred,"  it 
must  belong  to  one  or  another  of  the  established 
breeds.  But  anything  not  "pure-bred"  has  no 
recognized  standing,  or  market  value.  Without 
regard  to  the  merits  of  the  individual  the  mere 
fact  of  pedigree  registration  adds  a  definite  and 
not  inconsiderable  amount  to  the  monetary  value 
of  an  animal.  In  last  analysis  this  fact  is  to-day 
one  of  the  strongest  arguments  which  can  be  made 
to  the  farmer  in  favor  of  keeping  "pure-bred" 
animals. 

What  has  just  been  said  is  not  intended  in  any 
way  to  criticize,  or  belittle  the  importance  and 
value  of  the  "  pure-bred  "registry  system  of  develop- 
ing the  live-stock  industry  of  the  world.  I  merely 
wish  to  point  out  that  when  he  adopted  the 
system,  the  animal  breeder  took  upon  himself  along 
with  the  advantages  certain  very  real  restrictions 
to  the  freedom  of  his  breeding  operations,  which  the 
plant  breeder  has  escaped.  The  animal-breeding 
industry  of  the  world  has  developed  as  a  sys- 
tem of  pedigreed  aristocracy.  The  plant-breed- 
ing industry  is  developing  as  a  democracy.  The 
"social  position"  of  a  horse  or  a  cow  is  primarily 
determined  on  the  basis  of  whether  it  had  a  grand- 


176     MODES  OF  RESEARCH  IN  GENETICS 

father  or  not.  A  variety  of  oats  takes  its  place 
in  the  world  by  virtue  of  its  own  inherent  qualities, 
with  no  questions  asked  about  forebears  or  the 
orthodoxy  of  their  marital  relations.  Both  aris- 
tocracies and  democracies  have  their  advantages 
and  their  disadvantages  as  social  systems.  These 
merits  and  defects  are  just  as  real  and  effective 
in  their  operation  whether  the  ultimate  vital  unit 
of  the  system  be  a  man,  a  cow,  or  an  oat  plant. 

Owing  to  the  essentially  different  conditions  and 
methods  of  work  which  obtain  in  plant  breeding, 
this  field  is  able  to  reap  more  direct  benefits  of  a 
practical  character  from  the  advances  which 
have  been  made  in  the  science  of  genetics,  than  in 
animal  breeding.  In  the  creation  of  new  races  by 
hybridization  the  plant  breeder  can  and  does  take 
Mendelian  principles  as  a  direct  and  immediate 
guide.  He  has  made  Mendelism  a  working  tool 
of  his  craft. 

To  conclude :  ^^^lat  I  have  tried  to  do  in  this 
paper  is  to  discuss  the  relation  between  the  science 
of  genetics  and  the  practical  art  of  breeding  as 
they  actually  have  developed  and  now  exist.  At- 
tention has  been  directed  to  the  obvious  fact  that 
animal  breeding  has,  without  the  aid  of  genetic 
science,  attained  an  extremely  high  level  of  achieve- 
ment. Empirical  methods  can  only  have  been 
successful  when  they  were  fundamentally  in  accord 
with  natural  laws,  and  it  is  therefore  not  to  be  con- 
sidered surprising  that  the  recent  discoveries  of 


GENETICS  AND  BREEDING  177 

world-old  genetic  laws  have  not  radically  modified 
the  successful  animal  breeders'  methods.  In 
pointing  out  that  a  scientifically  trained  geneticist 
is  not  as  yet  an  absolutely  indispensable  necessity 
on  a  successful  animal-breeding  farm  I  have  no 
thought  or  desire  to  belittle  the  importance  of  the 
science  of  genetics.  My  zeal  and  enthusiasm  for 
the  advance  of  knowledge  in  this  field  know  no 
bounds.  This  attitude,  however,  furnishes  no 
reason  that  the  geneticist  should  delude  himself, 
or  by  rash  statements  hold  out  false  hopes  to  the 
breeder,  as  to  the  immediate  practical  importance 
of  some  of  the  recent  developments  in  the  science  of 
genetics.  All  knowledge  is  potentially  useful,  but 
the  fundamental  reason  for  undertaking  and  en- 
couraging research  in  genetics,  or  anything  else, 
is  not  because  what  one  gets  may  be  immediately 
useful,  but  because  it  is  knowledge. 


N 


INDEX 


Abstract  qualities  of  groups,  80. 

Accuracy  of  statistical  constants, 
53. 

Adami,  41. 

American  Breeders'  Association, 
159. 

Ancestral  elimination,  114. 

Ancestral  generations,  designa- 
tion of,  141. 

Ancestral  inheritance,  law  of,  11, 
13,  49,  66,  68. 

Anthropology,  42. 

Association,  degrees  of,  92. 

Assortative  mating,  10. 

Avuncular  matings,  126  ff. 

Bailey,  27. 

Bateson,  21,  27,  32. 

Beard  illustration,  13. 

Biochemical  method  in  inherit- 
ance, 40. 

Biological  implications  of  biome- 
try, 63. 

Biometric  constants,  57,  80. 

Biometric  method  in  genetics, 
9  ff ;  compared  with  Mendelian, 
19. 

Biometry,  9,  62  ff. 

Biometry  a  descriptive  method, 
12,  54,  62,  91. 

Births  of  children,  illustration,  92. 

Blood  transfusion,  9. 

Boring,  38. 

Boveri,  25. 

Brooks,  36. 

Brother  X  sister  mating.  111  ff. 


Bunsow,  102. 

Bursa  bursa-pastoris,  17. 

Card  drawing  illustration,  36. 
Carrel,  52. 
Castle,  17. 
Causation,  87. 
Center  of  group,  80. 
Ceratophyllvm,  58. 
Chapeaurouge,  102. 
Chromosomes  in  inheritance,  25, 

26,  31,  33-35. 
Clerk-Maxwell,  85. 
Coefficient    of    inbreeding,     110, 

113,    115,   119,    120,   125,    120, 

130,  132,  140,  145. 
Coefficient  of  relationship,  133  ff., 

145 ;  defined,  143. 
Comb  form,  inheritance  of,  173. 
Composition  of  groups,  79. 
Conklin,  7,  36. 
Contingency,  degree  of,  82. 
Cook,  105. 
Corn,  selection  experiments  with, 

16. 
Corn,  yield  of,  166. 
Correlation  coefficients,  15,  61,  69. 
Counting,  79,  130. 
Cousin  mating,  121  ff. 
Culture  in  vitro,  5. 
Curve  fitting,  logic  of,  21,  28. 
Curves   of  inbreeding,    110,    116, 

139. 
Cytological  method   in   genetics, 

24  ff. 
Cytoplasm  in  inheritance,  34. 


179 


180 


INDEX 


Danvin,  9,  161,  175. 
Description  as  philosophical  cat- 
egory, 13. 
Description  embryology,  37. 
Development,  5. 
Differentiation,  5. 
Diversity,  individual,  81. 
Doncaster,  34. 

Double  cousins,  121,  123,  125. 
Drosophila,  31. 

East,  16,  145,  149,  175. 

Eggs,  yield  of,  167. 

Ely,  166. 

Embryological  method  in  genet- 
ics, 35  S. 

Enriques,  14. 

Entwicklungsmechanik,  35. 

Expectation,  30. 

Experimental  method,  13,  18,  20, 
62. 

Factors,  multiple,  21,  27. 

Fallacy  of  qualitative  inference, 
28. 

Feathers,  8,  32. 

Fecundity,  17,  67. 

Fiddler  crab  illustration,  96. 

First-cousin  X  first-cousin  mat- 
ing, 121  ff. 

Fish,  150. 

Fluctuating  variation,  48. 

Free  generations,  108. 

Galton,  9,  10,  11,  17,  42,  43,  49. 

Gametogenesis,  4,  12,  24. 

Generation  interval  in  cattle, 
128. 

Genetics  and  breeding,  159  ff. 

Genetic  bearing  of  inbreeding  re- 
sults, 147  ff. 

Genetics,  practical  results  of, 
171  ff. 


Genotype,  65. 
Germ  cell,  4,  27. 
Group  description,  56. 
Gurwitsch,  36. 
Guyer,  41. 

Hagedoorn,  A.  C,  17. 

Hagedoorn,  A.  L.,  17. 

Hatai,  22. 

Hatschek,  41. 

Hayes,  16,  145,  149. 

Henry  VHI,  163. 

Heredity,  problem  of,  2  ff. ;  cate- 
gories of,  3. 

Heterogeneity  measured  by  cor- 
relation coefficient,  69. 

Hoesch,  102. 

Holstein  cattle,  144,  167. 

Homozygosis,  coefficient  of,  155. 

Homozygotes,  proportion  of,  in 
inbreeding,  149  ff. 

Horse,  107,  163. 

Hurst,  161. 

Inbreeding,  101  ff. 

Inbreeding,  calculation  of  co- 
efficients of.  111  ff;  curve  of, 
110,  116. 

Inbreeding,  definition  of,  106. 

Individual,  importance  of  in  bio- 
logical analysis,  48. 

Intensity  of  inheritance,  65. 

Jacobs,  155. 

Jennings,  6,  7,  13,  58,  67,  69,  89, 

149,  155. 
Jersey  cattle,  128,  129,  136  ff.,  144, 

169. 
Johannsen,  65,  67,  69. 

Kelvnn,  50. 

Kinds  of  knowledge  given  by 
statistics,  79. 


INDEX 


181 


King  Melia  Rioter  14th,  135  ff. 
Kossel,  41. 

Law  of  ancestral  inheritance,  11, 
13,  49,  66.  68;  biological  error 
in,  68. 

Lehndorff,  102,  107,  108. 

Like  parts,  58. 

Line  breeding,  105. 

Line  of  descent  in  calculating 
inbreeding,  130. 

Linkage  phenomena  in  inherit- 
ance, 31. 

Location  of  hereditary  deter- 
miners, 32. 

Low,  102,  108. 

Maternal  impressions,  172. 
Mendel,  161. 

Mendelian  mathematics,  21. 
Mendelian  method,  19  ff. 
Mendelism,  limitations  of,  23. 
Mendelism,  practical  bearings  of, 

162. 
Merz,  9,  76. 
Milk  production,   165,  166,  168, 

169. 
Miller,  168. 
Minot,  34. 
Morgan,  31,  32. 
Morphogenesis,  59. 
Mule  illustration,  90. 
Multiple  factor  hypothesis,  21. 

Nerve-muscle  physiology,  43. 
Nilsson-Ehle,  21. 

Oats,  yield  of,  166. 
von  Oettingen,  102,  107. 

Pangenesis,  9. 

Paramecium,  6,  58,  67. 

Parent  X  offspring  mating,  117  ff. 


Pawlow,  52. 

Pearl,  17,  29,  38,  53,  58.  66,  67, 
150. 

Pearson,  9,  10,  11,  13,  21,  22,  42, 
43,  49,  04. 

Pedigree  as  unit  of  analysis,  15. 

Pedigree  table,  brother  X  sister 
(hypothetical),  112;  parent  X 
offspring  (hypothetical),  118; 
single  cousins  (hypothetical), 
122;  double  cousins  (hypothet- 
ical), 123;  uncle  X  niece 
(hypothetical),  127;  Hess 
Weaver,  129;  King  Melia 
Rioter  14th,  142. 

Pfluger,  41. 

Phaenotype,  65. 

Phenomenal  indeterminism,  86. 

PhiUips,  17. 

Plant  and  animal  breeding  con- 
trasted, 175. 

Postembrj'onic  development,  37. 

Potatoes,  yield  of,  166. 

Poultry,  8,  17,  38,  66,  67,  167,  173. 

Practice  of  breeding,  161. 

Prediction  of  future  events,   94. 

Probable  error  concept,  50,  59, 
96. 

Probability,  science  of,  77. 

Punnett,  27,  32. 

"Purity  of  blood,"  173. 

Qualitative  and  quantitative  as- 
pects of  characters,  67. 
Quantification  of  biology,  50. 
Quetelet,  42. 

Rats,  selection  experiments  with, 

17. 
Redfield,  128. 

Reduplication  hypothesis,  27,  30. 
Regeneration,  5. 
Registration  of  Hve  stock,  176. 


182 


INDEX 


Relationship  coefficients,  133  "ff. ; 

defined,  143,  145. 
Resemblance  between  individuals, 

3,  10,  15,  64. 
Ritter,  55. 
Royce,  14,  74,  85,  88. 

Saturation,  172. 

Scott,  165. 

Segregation,  25,  45,  174. 

Selection,  15,  48,  175. 

Sex  chromosomes,  26. 

ShuU,  17. 

Single  cousins,  121,  122,  125. 

SkewTiess,  81. 

Somatogenesis,  5,  12,  35. 

Specificity,  germinal,  8,  12. 

Specificity,  somatogenic,  5,  8. 

Spillman,  24. 

Statistical  knowledge,  73  ff. ;  an- 
alysis of,  79;  exactness  of, 
81. 

Statistical  method,  possibilities 
of,  83. 

Statistical  probabiUties,  92. 


Strang,  102. 
Surface,  16,  58,  66. 
Symmetry  of  distributions,  81. 
Systematic  zoology,  56. 

Telegony,  172. 

Tobacco,    selection    experiments 

with,  16. 
Tretsven,  168. 
Trow,  27. 

Uncle  X  niece  mating,  126  ff. 
Unit  characters,  173. 

Valentine,  166. 
Variability,  8. 
Ven\'orn,  41. 

Weldon,  42. 
Wheat,  yield  of,  166. 
Whitten,  166. 
Williams,  166. 
Wilson,  33. 

Yule,  22,  71. 


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Section  I  —  Inorjianic  Evolution.  Geographical  Distribution 

The  Evolution  of  Matter.  Part  II      Theories  of  Evolution 

Section  II  —  Oganic  Evolution  Section  III  —  Superorganic  Evolution. 
Part  I      The  Facts  of  Evolution  Social  Evolution. 

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"  I  find  that  it  i?  a  very  useful  study  for  an  introduction  to  the  subject.  Professor 
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